模型敏感度与不确定性分析：量化与沟通方法

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本章深入探讨了模型敏感性和不确定性分析在信息技术中的关键作用。任何模型的有效性都与其输出的精确度和可靠性紧密相关，然而，由于模型本质上是对现实世界的简化抽象，且精确输入数据的获取极其有限，模型输出不可避免地带有一定程度的不精确和不确定性。这些不确定性来源于多个方面： 1. **自然变异**（Natural Variability）：自然环境因素的随机变化，如气候变化、水文条件等，对模型预测结果有直接影响。 2. **知识不确定性**（Knowledge Uncertainty）： - **参数值不确定性**（ParameterValue Uncertainty）：模型参数的设定可能存在不确定性，如基于专家意见或历史数据估计的参数值。 - **模型结构与计算错误**（Model Structural and Computational Errors）：模型设计缺陷或算法误差可能导致预测偏差。 3. **决策不确定性**（Decision Uncertainty）：模型应用时，决策者的主观判断和偏好也会影响结果的不确定性。 4. **敏感性和不确定性分析**（Sensitivity and Uncertainty Analyses）： - **不确定性分析**（Uncertainty Analyses）：通过统计方法识别和量化模型及参数的不确定性，帮助评估输出结果的可信度。 - **敏感性分析**（Sensitivity Analyses）：衡量模型输出对输入变量变化的响应程度，常用方法包括： - **敏感系数**（Sensitivity Coefficients）：衡量单个参数对结果影响的大小。 - **确定性敏感性分析**（Deterministic Sensitivity Analysis）：步骤包括确定关键输入变量、计算敏感度指标等。 - **多重错误和交互效应**（Multiple Errors and Interactions）：考虑多个不确定因素之间的相互作用。 - **第一阶敏感性分析**（First-Order Sensitivity Analysis）：逐个考察输入变量对输出的影响。 - **部分因子试验设计法**（Fractional Factorial Design Method）：有效减少试验次数以分析敏感性。 - **蒙特卡洛模拟**（Monte Carlo Sampling Methods）：随机抽样技术，模拟大量可能情况以估计不确定性范围。 5. **性能指标不确定性**（Performance Indicator Uncertainties）：关注如何量化和比较不同性能指标的不确定性，比如目标设定的不确定性以及指标分布差异。 6. **沟通模型输出不确定性**（Communicating Model Output Uncertainty）：将分析结果有效地传达给利益相关者，确保他们理解并信任模型预测的局限性。总结起来，模型敏感性和不确定性分析是IT项目中不可或缺的组成部分，它帮助我们理解和管理模型的预测风险，从而做出更明智的决策。通过结合各种分析方法，我们可以提高模型的可靠性和实用性，降低潜在的负面影响。

Note that the time series may even contain values outside

the range ‘b’ defined in Figure 9.4 if the confidence level of

that range is less than 100%. Confidence intervals associ-

ated with less than 100% certainty will not include every

possible value that might occur.

3.2. Knowledge Uncertainty

Referring to Figure 9.3, knowledge uncertainty includes

model structure and parameter value uncertainties. First

we consider parameter value uncertainty including

boundary condition uncertainty, and then model and

solution algorithm uncertainty.

3.2.1. Parameter Value Uncertainty

A possible source of uncertainty in model output results

from uncertain estimates of various model parameter

values. If the model calibration procedure were repeated

using different data sets, different parameter values would

result. Those values would yield different simulated sys-

tem behaviour and, thus, different predictions. We can call

this parameter uncertainty in the predictions because it is

caused by imprecise parameter values. If such parameter

value imprecision were eliminated, then the prediction

would always be the same and so the parameter value

uncertainty in the predictions would be zero. But this does

not mean that predictions would be perfectly accurate.

In addition to parameter value imprecision, uncertainty

in model output can result from imprecise specification

260 Water Resources Systems Planning and Management

of boundary conditions. These boundary conditions

may be either fixed or variable. However, because they

are not being computed on the basis of the state of the

system, their values can be uncertain. These uncertainties

can affect the model output, especially in the vicinity of the

boundary, in each time step of the simulation.

3.2.2. Model Structural and Computational Errors

Uncertainty in model output can also result from errors in

the model structure compared to the real system, and

approximations made by numerical methods employed in

the simulation. No matter how good our parameter value

estimates, our models are not perfect and there is a resid-

ual model error. Increasing model complexity in order to

more closely represent the complexity of the real system

may not only add to the cost of data collection, but may

also introduce even more parameters, and thus even more

potential sources of error in model output. It is not an

easy task to judge the appropriate level of model com-

plexity and to estimate the resulting levels of uncertainty

associated with various assumptions regarding model

structure and solution methods. Kuczera (1988) provides

an example of a conceptual hydrological modelling exer-

cise with daily time steps where model uncertainty dom-

inates parameter value uncertainty.

3.3. Decision Uncertainty

Uncertainty in model predictions can result from

unanticipated changes in what is being modelled. These

can include changes in nature, human goals, interests,

activities, demands and impacts. An example of this is the

deviation from standard or published operating policies

by operators of infrastructure such as canal gates, pumps

and reservoirs in the field, as compared to what is

specified in documents and incorporated into the water

systems models. Comparing field data with model data

for model calibration may yield incorrect calibrations if

operating policies actually implemented in the field differ

significantly from those built into the models. What do

operators do in times of stress?

What humans will want to achieve in the future may

not be the same as what they want today. Predictions of

people’s future desires are clearly sources of uncertainty.

system performance indicator

time

E020110

Figure 9.5. Typical time series of model output or system

performance indicator values that are the result of input data

variability and possible imprecision in input data

measurement, parameter value estimation, model structure

and errors in model solution algorithms.

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WATER RESOURCES SYSTEMS PLANNING AND MANAGEMENT – ISBN 92-3-103998-9 – © UNESCO 2005

Model Sensitivity and Uncertainty Analysis 261

A perfect example of this can be seen in the very flat

Greater Everglades region of south Florida in the United

States. Fifty years ago, folk wanted the swampy region

protected from floods and drained for agricultural and

urban development. Today many want just the opposite, at

least where there are no human settlements. They want to

return to a more natural hydrological system with more

wetlands and unobstructed flows, but now for ecological

restoration reasons, which were not a major concern

or much appreciated some half a century ago. Once the

mosquitoes return, and if the sea level continues to rise,

future populations who live there may want more flood

control and drainage again. Who knows? Complex and

changing social and economic processes influence human

activities and their demands for water resources and envi-

ronmental amenities over time. Some of these processes

reflect changes in local concerns, interests and activities,

but population migration and many economic activities

and social attitudes can also reflect changing national and

international trends.

Sensitivity scenarios that include human activities can

help define the effects of those activities within an area.

Careful attention should be given to the development of

these alternative scenarios so that they capture the real

forces or stresses that the system may face. The history

of systems studies are full of examples where the issues

studied were overwhelmed by much larger social forces

resulting from, for example, the relocation of major

economic activities, an oil embargo, changes in national

demand for natural resources, economic recession, an

act of terrorism or even war. One thing is certain: the

future will be different than the past, and no one knows

just how.

Surprises

Water resources managers may also want to consider how

vulnerable a system is to undesirable environmental

surprises. What havoc might an introduced species

like the zebra mussel invading the Great Lakes of

North America have in a particular watershed? Might some

introduced disease suddenly threaten key plant or animal

species? Might management plans have to be restructured

to address the survival of species such as salmon in the

Rhine River in Europe or in the Columbia River in North

America? Such uncertainties are hard to anticipate when

by their nature they will truly be surprises. But surprises

should be expected. Hence system flexibility and adapt-

ability should be sought to deal with changing manage-

ment demands, objectives and constraints.

4. Sensitivity and Uncertainty

Analyses

An uncertainty analysis is not the same as a sensitivity

analysis. An uncertainty analysis attempts to describe

the entire set of possible outcomes, together with their

associated probabilities of occurrence. A sensitivity analysis

attempts to determine the change in model output

values that results from modest changes in model input

values. A sensitivity analysis thus measures the change in

the model output in a localized region of the space of

inputs. However, one can often use the same set of model

runs for both uncertainty analyses and sensitivity analyses.

It is possible to carry out a sensitivity analysis of the model

around a current solution, and then use it as part of a first-

order uncertainty analysis.

This discussion begins by focusing on some methods

of uncertainty analysis, then reviews various ways of

performing and displaying sensitivity analyses.

4.1. Uncertainty Analyses

Recall that uncertainty involves the notion of random-

ness. If a value of a performance indicator or performance

measure, like the phosphorus concentration or the depth

of water at a particular location, varies, and this variation

over space and time cannot be predicted with certainty, it

is called a random variable. One cannot say with certainty

what the value of a random variable will be but only the

likelihood or probability that it will be within some spec-

ified range of values. The probabilities of observing par-

ticular ranges of values of a random variable are described

or defined by a probability distribution. There are many

types of distributions and each can be expressed in several

ways as presented in Chapter 7.

Suppose the random variable is denoted as X. As dis-

cussed in Chapter 7, if the observed values of this random

variable can only have discrete values, then the probability

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