To improve the efficiency of flood early warning systems (FEWS), it is
important to understand the interactions between natural and social systems.
The high level of trust in authorities and experts is necessary to improve
the likeliness of individuals to take preparedness actions responding to
warnings. Despite many efforts to develop the dynamic model of human and
water in socio-hydrology, no socio-hydrological models explicitly simulate
social collective trust in FEWS. Here, we develop the stylized model to
simulate the interactions of flood, social collective memory, social
collective trust in FEWS, and preparedness actions responding to warnings by
extending the existing socio-hydrological model. We realistically simulate
the cry wolf effect in which many false alarms undermine the credibility of
the early warning systems and make it difficult to induce preparedness
actions. We found that (1) considering the dynamics of social collective trust in
FEWS is more important in the technological society with infrequent flood
events than in the green society with frequent flood events; and (2) as the
natural scientific skill to predict flood events is improved, the efficiency
of FEWS gets more sensitive to the behavior of social collective trust, so
that forecasters need to determine their warning threshold by considering
the social aspects.
Introduction
The number of severe flood events is expected to increase in many regions
due to climate change (Hirabayashi et al., 2013, 2021). Based on the advances
of weather forecasting (e.g., Bauer et al., 2015; Miyoshi et al., 2016; Sawada
et al., 2019) and hydrodynamic modeling (e.g., Yamazaki et al., 2011; Trigg et al., 2016), flood early warning systems (FEWS) have become a promising tool
to efficiently mitigate the damage of severe floods. However, to maximize
the potential of FEWS, it is crucially important to understand the
interactions between flood and social systems. The likeliness of individuals
to take preparedness actions responding to flood warnings strongly depends
on the individual's risk perception, which is controlled by the complex
interaction between natural hazards and stakeholders (Wachinger et al., 2013).
In the literature of weather forecasting, the “cry wolf effect” has been
intensively investigated as an important interaction between weather
prediction and social systems. In Aesop's fable, “The Boy who Cried
Wolf”, a young boy repeatedly tricks neighboring villagers into believing
that a wolf is attacking the sheep. When a wolf actually appears and the
young boy seriously calls for help, the villagers no longer trust the
warning and fail to protect their sheep. Many false alarms undermine the
credibility of the early warning systems. The cry wolf effect on mitigation
and protection actions against meteorological disasters has been
investigated in economics, sociology, and psychology. Many previous studies
have found and quantified the cry wolf effects in meteorological disasters.
Simmons and Sutter (2009) performed econometric analysis of a disaster
database and revealed that tornadoes that occurred in areas with higher
false alarm ratio killed and injured more people. Ripberger et al. (2015)
performed a web-based questionnaire survey and revealed that subjective
perceptions of warning systems' accuracy are systematically related to trust
in a weather agency and stated responses to warnings. Trainor et al. (2015)
performed large-scale telephone interviews and revealed the significant
relationship between actual false alarm ratio and behavioral responses to
tornado warnings. Jauernic and van den Broeke (2017) revealed that the odds
of students initialing sheltering decreases nearly 1 % for every 1 %
increase in perceived false alarm ratio based on their online questionnaire
survey of 640 undergraduate students. Roulston and Smith (2004) found that
the warning threshold of the actual weather warning systems can be justified
only if the cry wolf effects were considered. This finding implies that many
forecasters believe the existence of the cry wolf effects, and the design of
early warning systems is affected by how the cry wolf effects are
considered. It should be noted that while these previous works supported the
cry wolf effect as an important factor to be considered for the design of
warning systems, some studies discussed the myth of cry wolf effects,
implying that they do not exist. For example, LeClerc and Joslyn (2015)
performed a psychological experiment in which participants decided whether
to apply salt brine to a town's roads to prevent icing according to weather
forecasting. In their experiment, the effects of false alarms are so small
that they found no evidence suggesting lowering false alarm ratio
significantly increases compliance with weather warnings. Lim et al. (2019)
performed an online questionnaire survey and found no significant
relationship between actual false alarm ratio and responses to warnings. In
addition, they found that the increase of perceived false alarm ratio
enhanced protective behavior, which contradicted the other works. Although
Trainor et al. (2015) supported the existence of the cry wolf effects, they
also found that there is a wide variation in public definition of false
alarms, and actual false alarm ratio does not predict perception of false
alarm ratio. Although the existence of the cry wolf effect is still
debatable due mainly to the lack of field data and the ambiguity of the
quantification of the public perception of false alarms, the current
evidence suggests the importance of understanding the effect of false alarms on
behavioral responses to warning in order to design efficient flood early
warning systems.
Socio-hydrology is an emerging research field contributing to understanding
the interactions between flood and social systems (Sivapalan et al., 2012,
2014; Di Baldassarre et al., 2019). The primary approach of socio-hydrology
is to develop the dynamic model of water and human. Many socio-hydrological
models used social preparedness as a key driver of human–water interactions
(e.g., Di Baldassarre et al., 2013; Viglione et al., 2014; Ciullo et al., 2017;
Yu et al., 2017; Albertini et al., 2020). The pioneering work of Girons Lopez
et al. (2017) revealed the effect of social preparedness on the efficiency
of FEWS. Their main finding is that social preparedness is an important
factor for flood loss mitigation especially when the accuracy of the
forecasting system is limited. However, to our best knowledge, the existing
socio-hydrological models simulated social preparedness as a function of
social collective memory or personal experience of past disasters, and they
considered no effect of trust in authorities and experts. Therefore, the cry
wolf effect cannot be analyzed in the existing models. The systematic review
of Wachinger et al. (2013) indicated that both personal experience of past
disasters and trust in authorities and experts have substantial impact
on risk perception. It is crucially important to include the social
collective trust in FEWS in the socio-hydrological model to improve the
design of FEWS considering social system dynamics.
The aim of this study is to develop the stylized model of the responses of
social systems to FEWS as a simple extension of Girons Lopez et al. (2017). By modeling the dynamics of social collective trust in FEWS as a
function of the recent success and failure of the forecasting system, we
realistically simulate the cry wolf effect. By analyzing our newly developed
model, we provide useful implication to maximize the potential of FEWS
considering social system dynamics.
Model
Here, we slightly modified the model proposed by Girons Lopez et al. (2017).
For brevity, the detailed explanation of equations shared with Girons Lopez
et al. (2017) is omitted in this paper. See Gironz Lopez et al. (2017) and
references therein for the complete description, including empirical evidence
which supports each equation.
A synthetic time series of river discharge is generated. Following Girons
Lopez et al. (2017), a simple bivariate gamma distribution, Γ, is used:
Q∼Γ(κcθc),
where Q is maximum annual flow [L3 T-1]. The bivariate gamma
distribution is characterized by shape κc and scale θc.
This maximum annual flow, Q, is forecasted. In our model, the ensemble flood
forecasting system (e.g., Cloke and Pappenberger, 2009) is installed, and the
probabilistic forecast can be issued. The forecast probability distribution,
F, is calculated by the following:
F∼N(Q+Nμm,σm2,Nμv,σv2),
where N(.) is the Gaussian distribution, Nμm,σm2 controls the prediction accuracy, and Nμv,σv2 controls the prediction precision. Negative Nμv,σv2 is truncated to 1.0×10-6 to prevent from
obtaining negative values of variance. While Girons Lopez et al. (2017)
change μm in their simulation, we set μm=0 assuming the
forecast is unbiased. While Girons Lopez et al. (2017) used the bivariate
gamma distribution to model the prediction precision, we used the Gaussian
distribution to make it easier to interpret results. Although this
simplification of the forecasting system unrealistically assigns non-zero
probability to negative values of discharge, it does not affect the process
dynamics since the model evolution depends only on whether forecasted
discharge is above the damage threshold, as we explain in the next
paragraph.
Summary of the outcomes of the flood early warning system. Loss by
each outcome is also shown (see also Sect. 2).
There is a damage threshold [L3 T-1], δ, which is the proxy
of levee height. When Q>δ, flood occurs. The forecast system
calculates the probability of river discharge exceeding δ, and issues
a warning if this probability of exceedance, P, is larger than a predefined
probability threshold, π. Table 1 summarizes four different outcomes of
forecasting: true positive, false positive, false negative, and true
negative. When forecasters choose lower π, they issue many warnings
with low forecasted probability of flooding, which inevitably increases
false alarms. When forecasters choose higher π, they can reduce the
number of false alarms by issuing the smaller number of warnings, which
inevitably increases missed events.
Based on these four different outcomes shown in Table 1, damages and costs
are calculated. Flood damage is assumed to be negligible when river
discharge is smaller than a damage threshold (i.e., Q<δ). When Q≥δ, the damage function is defined as a simple exponential function,
which is often used in the socio-hydrological literature (e.g., Di
Baldassarre et al., 2013):
DQ=0(Q<δ)1-e-Q-δβ(Q≥δ),
where DQ is damage [.], β is a model parameter [L-3 T]. If a
flood event is successfully forecasted and a warning is issued (i.e., P≥π), this damage is mitigated by preparedness actions such as evacuation
and safekeeping of assets. Note that preparedness actions which are not
triggered by FEWS were not considered in this stylized model to focus only
on the impact of social preparedness on the efficiency of FEWS. How much
damage can be mitigated depends on social preparedness, Pr [.]. The
mitigated damage (called residual damage in Girons Lopez et al., 2017),
Dr [.], is calculated by the following:
Dr=DQe-Prln(1α0),
where α0 is a model parameter [.] which determines the minimum
possible damage. In summary, the flood damage [.], D, can be described by
Eq. (5):
D=0(Q<δ)1-e-Q-δβ(Q≥δ and P<π)1-e-Q-δβe-Prln1α0(Q≥δ and P≥π).
Whenever a warning is issued, the cost [.], C, arises from mitigation and
protection actions. Whenever a warning is issued, C is included in the
total loss. Following Girons Lopez et al. (2017), we assumed that the cost
is calculated by
C=0P<πηQP≥π,
where η is a parameter [L-3 T]. Note that this cost has been found
to be negligibly small compared with avoidable damage. For instance,
Schroter et al. (2008) showed that the cost C is approximately 2 % of
avoidable damage. In previous works, this cost was often neglected (e.g.,
Pappenberger et al., 2015; Hallegatte, 2012). Although Gironz Lopez et al. (2017) assumed there are significant costs of mitigation and protection
actions, we will discuss how differently their model and our newly proposed
model work with no mitigation costs (i.e., η=0) and with the
original settings of Gironz Lopez et al. (2017).
The dynamics of social preparedness, Pr, in this study is different
from Girons Lopez et al. (2017). We assumed that the social preparedness
consisted of social collective memory and social collective trust in FEWS,
Pr(t)=γE(t)+1-γT(t),
where E(t) and T(t) are social collective memory [.] and
social collective trust [.] in FEWS at time t, respectively. γ is
a model parameter [.] that weights E(t) and T(t). Social
collective memory is shared knowledge and information about past flood
disasters that occurred in a community. In many socio-hydrological models, social
collective memory is driven by the recency of past flood experience.
Following Girons Lopez et al. (2017), the dynamics of social collective
memory is described by the following:
Et+1=E(t)-λE(t)(D=0)E(t)+χD(D>0),
where λ and χ are model parameters [.]. When E becomes
larger than 1, it is truncated to 1.
Social collective trust is defined as shared knowledge and perception of the
reliability of information issued from authorities. We assumed that social
collective trust in FEWS is affected by the recent accuracy of FEWS.
Previous studies pointed out that the recent forecast accuracy and false
alarm ratio affected the performance of preparedness actions (Simmons and
Sutter, 2009; Trainor et al., 2015; Ripberger et al., 2015; Jauernic and van
den Broeke, 2017). In the controlled experiment of LeClerc and Joslyn (2015),
medium-range trust ratings are increased by decreased false alarm levels.
Their experiments revealed that trust ratings are based on the pattern of
forecasts and observations over the previous month. It is reasonable to
assume that trust in FEWS increases (decreases) when prediction succeeds
(fails). We propose the following simple equation to describe the dynamics
of social collective trust in FEWS:
Tt+1=T(t) for true negativeT(t)+τTP for true positiveT(t)-τFN for false negativeT(t)-τFP for false positive,
where τTP, τFN, and τFP are positive parameters
[.]. When T becomes larger than 1, it is truncated to 1. When T becomes
smaller than 0, it is truncated to 0. By changing the value of these
parameters, we can change the sensitivity of social collective trust in FEWS
to the accuracy of FEWS. We will analyze the behavior of our model
associated with several different combinations of these three parameters.
In our Eqs. (7–9), we can consider both social collective memory and
social collective trust to analyze behavioral responses to warnings. For
instance, please assume that a severe flood occurs and substantially damages
a community, and this flood event cannot be predicted. In this case, social
collective memory increases due to the large damage (Eq. 8). This
increase of social collective memory E(t) contributes to
increasing social preparedness towards the next severe flood event
(Eq. 7). However, the failure of predicting this flood event
decreases social collective trust in FEWS and authorities related to warning
systems (Eq. 9), which negatively impacts to the capability of a
community to deal with the next flood event by decreasing social
preparedness (Eq. 7).
If social preparedness is determined only by social collective memory as
Girons Lopez et al. (2017) proposed, small social collective memory directly
results in insufficient social preparedness actions. In our proposed model,
high social collective trust in FEWS can induce social preparedness actions
even if a community loses past flood experiences to some extent (Eq. 7). However, if a weather agency repeatedly issues false alarms, social
collective trust in FEWS decreases (Eq. 9), which negatively impacts
on social preparedness (Eq. 7). Therefore, the dynamics of social
preparedness in our proposed model is greatly different from Girons Lopez et al. (2017).
The additive form of the Eq. (7) implies that preparedness actions are
taken even if either social collective memory E(t) or social
collective trust T(t) goes to zero. Note that E(t)≈0
does not mean that a community does not know the existence of a flood event,
while it means most citizens have never experienced water levels above
damage thresholds by themselves. Many disasters prevention measures such as
education, evaluation drills, and FEWS are designed to let people take
preparedness actions even if they have no personal experiences of flood
disasters. Forecasters expect that people take preparedness actions based on
information from their trusted authorities even if they have never
experienced damages themselves. To evaluate the effectiveness of these
measures, Pr(t)=0 with E(t)=0 is not an
appropriate behavior of the model, although the effectiveness of FEWS highly
depends on E(t) as Girons Lopez et al. (2017) found.
Therefore, we chose the additive form of the Eq. (7) rather than the
other simple alternatives such as multiplicative forms.
Fixed model parameters.
DescriptionEquationValuesκcshape of the bivariate gamma distribution to generate river discharge time series(1)2.5θcscale of the bivariate gamma distribution to generate river discharge time series(1)0.08μmmean of prediction error(2)0βparameter of the damage function(3)0.2α0minimum residual damage fraction(4)0.2λsocial collective memory decay rate(8)0.028χpsychological shock magnitude(8)1.0
Many of the model parameters are fixed in our analysis. Table 2 summarizes
the description and values of the fixed parameters. These parameters are not
focused on in our analysis, and we chose their values from the previous
works. The values of κc, θc, α0, and χ are same as Girons Lopez et al. (2017). We set μm=0 assuming the
forecast is unbiased (see also Eq. 2 and its description). Our
specified β is within the range proposed by Girons Lopez et al. (2017). In addition, the results of Girons Lopez et al. (2017) indicated
that this parameter is not sensitive to relative loss. We set λ
assuming that social collective memory has 25-year half-life, which is within
the range of previously quantified values (e.g., Fanta et al., 2019;
Barendrecht et al., 2019). Some parameters are changed in our analysis to
check their sensitivity to the performance of FEWS. Those parameters are
explained in the next section.
Experiment designMetrices
We used several metrices to evaluate the performance of FEWS. The purpose of
FEWS is to reduce the total loss (D+C). We used the relative loss as
Girons Lopez et al. (2017) did. The relative loss, Lr, is defined by Eq. (10):
Lr=LFEWSLnoFEWS.
We performed the long-term (1000-year) numerical simulation by solving
Eqs. (1–9) and calculated the total loss, LFEWS. We also performed
the simulation without FEWS in which flood damage is always calculated by
Eq. (3) and D is always equal to DQ. The total loss of this
additional simulation is defined as LnoFEWS. The relative loss measures the efficiency of FEWS.
In addition to relative loss, we used hit rate, false alarm ratio, and
threat score to evaluate the prediction accuracy which is not related to
social system dynamics. They are defined by Eqs. (11–13):
11hit rate=OTPOTP+OFN12false alarm ratio=OFPOFP+OTP13threat score=OTPOTP+OFP+OFN,
where OTP, OFN, and OFP are the total number of true
positive, false negative, and false positive events, respectively.
Simulation settings
We firstly compared the original model proposed by Girons Lopez et al. (2017) with our modified model. When we set γ=1 in Eq. (7), our
model reduces to Girons Lopez et al. (2017) since we have no contributions
of social collective trust in FEWS to social preparedness. In this paper,
this original model is hereafter called the GL (Gironz Lopez) model. On the other hand,
when we set γ=0.5 in Eq. (7), our model considers both social
collective memory and social collective trust in FEWS with same weights to
calculate social preparedness. There is no existing knowledge about the
relative importance of social collective memory and social collective trust.
Assuming the same weights gives us the most straightforward interpretation
of the contributions of social collective trust and memory to social
preparedness and the total loss by floods, since we do not need to consider
asymmetric contributions of the two factors in Eq. (7). Therefore,
γ=0.5 is appropriate to analyze the essential behavior of our
proposed model. This new model with γ=0.5 is hereafter called the
SKK (Sawada, Kanai, and Kotani) model. The behavior of the models with the different γ is also
discussed in the supplement material.
Model parameters in Experiment 1.
DescriptionEquationValuesσmstandard deviation of prediction error(2)0.075μvmean of prediction precision(2)0.15σvstandard deviation of prediction precision(2)0.075δdamage threshold(3, 5)0.35πpredefined probability threshold(5, 6)0.40ηcost parameter(6)0.02γparameter controlling weights of social collective memory and trust(7)1 (GL model) 0.5 (SKK model)τTPincrement of trust for true positive(9)0.1τFNincrement of trust for false negative(9)0.1τFPincrement of trust for false positive(9)0.1
In Experiment 1, the time series of state variables of the two models are
compared to demonstrate how differently the SKK and GL models work. The
parameter variables in Experiment 1 are shown in Table 3. The initial
conditions of E and T are randomly chosen and set to 0.49 and 0.77,
respectively.
Model parameters in Experiment 2.
DescriptionEquationValues exp2.1exp2.2exp2.3exp2.4exp2.5exp2.6σmstandard deviation of prediction error(2)0.050.0750.050.050.0750.05μvmean of prediction precision(2)0.050.150.050.050.150.05σvstandard deviation of prediction precision(2)0.0250.0750.0250.050.0750.025δdamage threshold(3, 5)0.350.350.350.350.350.35ηcost parameter(6)000.1000.1γparameter controlling weights of social collective memory and trust(7)1(GL model)1(GL model)1(GL model)0.5(SKK model)0.5(SKK model)0.5(SKK model)τTPincrement of trust for true positive(9)0.10.10.10.10.10.1τFNincrement of trust for false negative(9)0.10.10.10.10.10.1τFPincrement of trust for false positive(9)0.10.10.10.10.10.1
We mainly focused on the relationship between relative loss and a predefined
probability threshold, π. This warning threshold is important for
forecasters to determine whether they require general citizens to take
preparedness actions. In Experiment 2, we used the same damage
threshold, δ, as Girons Lopez et al. (2017), and compared the
relationship between relative loss and predefined probability thresholds in
the GL model with that in the SKK model under the different prediction
skills and the cost parameter η. The settings of the parameters in
Experiment 2 can be found in Table 4. The prediction skill is controlled by
σm, μv, and σv. The greater values of
these parameters provide inaccurate prediction. We prepared two sets of the
parameter for relatively accurate and inaccurate prediction systems (see
Table 4). Following the settings of Girons Lopez et al. (2017), we set η=0.1. In addition, we also performed the numerical simulation with η=0 (i.e., negligible costs of mitigation and protection actions), which is
more consistent to the published literature than the original settings (see
Sect. 2).
Model parameters in Experiment 3.
DescriptionEquationValues exp3.1exp3.2exp3.3exp3.4σmstandard deviation of prediction error(2)0.050.050.050.05μvmean of prediction precision(2)0.050.050.050.05σvstandard deviation of prediction precision(2)0.0250.0250.0250.025δdamage threshold(3, 5)0.200.200.450.45ηcost parameter(6)0.020.020.020.02γparameter controlling weights of social collective memory and trust(7)1 (GL model)0.5 (SKK model)1 (GL model)0.5 (SKK model)τTPincrement of trust for true positive(9)0.10.10.10.1τFNincrement of trust for falsenegative(9)0.10.10.10.1τFPincrement of trust for falsepositive(9)0.10.10.10.1
In Experiment 3, we also compared the GL and SKK models under different
damage thresholds, δ. In socio-hydrology, previous works focused on
the difference between “green” and “technological” society (Ciullo et al., 2017). In green society, risk is dealt with mainly by non-structural
measures. In this society, the flood protection level is so low that many
flood events occur, which increases social collective memory of flood
events. In technological society, the flood protection level is so high that
risk can be dealt with by structural measures and non-structural
measures. Since flood events occur less frequently in the technological
society, the high level of social collective memory cannot be maintained. By
changing the damage threshold, we analyzed how differently the GL and SKK
models behave in the different society. The settings of the parameters in Experiment 3 can be found in Table 5. From the original value of the
damage threshold proposed by Girons Lopez et al. (2017) (i.e., δ=0.35), we decreased and increased δ to simulate the green and
technological societies, respectively (see Table 5).
Model parameters in Experiment 4.
DescriptionEquationValuesσmstandard deviation of prediction error(2)0.05 (accurate forecast) 0.075 (inaccurate forecast)μvmean of prediction precision(2)0.05 (accurate forecast) 0.15 (inaccurate forecast)σvstandard deviation of prediction precision(2)0.025 (accurate forecast) 0.075 (inaccurate forecast)δdamage threshold(3, 5)0.20 (green society) 0.45 (technological society)ηcost parameter(6)0.02γparameter controlling weights of social collective memory and trust(7)1 (GL model)[τTPτFNτFP]increment of trust for true positive, false negative, and false positive(9)[0.1, 0.1, 0.1] (blue lines in Fig. 4a–h) [0.1, 0.1, 0.8] (orange lines in Fig. 4a–h) [0.1, 0.8, 0.1] (green lines in Fig. 4a–h)
In Experiment 4, we analyzed only the SKK model. The primary purpose of
this Experiment 4 is to find the optimal predefined probability threshold,
which minimizes relative loss, in not only different society and prediction
accuracy but also different combinations of parameters related to the
dynamics of social collective trust in FEWS (i.e., τTP,τFN, and τFP in Eq. 9). The settings of the parameters in Experiment 4 can be found in Table 6. We analyzed how the optimal
warning threshold is changed by changing τFN and τFP (see
Table 6).
In Experiments 2–4, we performed the 250-member Monte Carlo simulation by
randomly perturbing a predefined probability threshold, π, and the
initial conditions of social collective memory and social collective trust
in FEWS. We used the same random seed to generate 250-member Monte Carlo
simulation in each experiment, so that the differences between experiments do not depend on random processes. We analyzed the sensitivity of the
efficiency of FEWS to predefined probability thresholds.
Time series of (a) the GL model and (b) the SKK model of
Experiment 1 (see Sect. 3 and Table 2 for model parameters). Black,
purple, and pink lines are social preparedness, half of social collective
memory, and half of social collective trust in FEWS, respectively. Since
social preparedness is identical to social collective memory and social
collective trust is not considered in the GL model, there are no purple and
pink lines in (a). Note that the sum of half of social collective memory and
half of social collective trust in FEWS is social preparedness in (b). Blue,
red, and green bars show total loss by the outcomes of false positive, false
negative, and true positive, respectively (see Table 2).
Results
Figure 1 shows the time series of social preparedness of the GL and SKK
models in Experiment 1 (see Table 3). The purpose of Fig. 1 is to
demonstrate how differently the SKK and GL models work by showing the
time series. While Fig. 1 shows the subset of the entire time series to
clearly demonstrate the differences between two models, the entire
time series can be found in Fig. S1 in the Supplement. In the GL
model (Fig. 1a), social preparedness (black line) increases when flood
occurs (red and green bars) and is not affected by false alarms (blue bars).
In the SKK model (Fig. 1b), false alarms negatively impact social
preparedness by reducing social collective trust in FEWS (pink line). From
t=430 to t=440, consecutive false alarms substantially decrease social
collective trust in FEWS and social preparedness, so that the damage of
severe flood at t=452 in the SKK model is larger than that in the GL model
despite the accurate warning being issued. It is the cry wolf effect.
The relationship between relative loss and predefined probability
thresholds in (a) the GL model and (b) the SKK model in Experiment 2. In
(a), blue, orange, and green lines show the results of Experiments 2.1,
2.2, and 2.3, respectively. In (b), blue, orange, and green lines show the
results of Experiments 2.4, 2.5, and 2.6, respectively. Each dot shows the
result of the individual Monte Carlo simulation and we smoothed them by
Gaussian process regression. See also Table 4 for detailed parameter
settings.
Figure 2a shows the relationship between relative loss and predefined
probability thresholds simulated by the GL model in Experiment 2 (see
Table 4). We firstly assumed that there is no cost of the mitigation and
protection action, and is the relatively accurate prediction system (Experiment 2.1; see Table 4). In this case, FEWS can minimize the relative
loss with the extremely small predefined probability thresholds (blue line).
When we degrade the prediction skill (Experiment 2.2; see Table 4),
forecasters still maintain the same level of relative loss by setting low
(or zero) predefined probability thresholds, issuing many false alarms
(orange line). It is apparently unrealistic. In the framework of the GL
model, this unrealistic model's behavior can be eliminated by setting the
high cost of the mitigation and protection action responding to the issued
warning. When we assume the high cost of preparedness actions (Experiment 2.3; see Table 4), the small predefined probability threshold
induces high relative loss (green line). Forecasters need to avoid issuing
false alarms when the cost which should be paid with false alarms is large.
Note that the total costs of mitigation and protection actions with η=0.1 in Experiment 2.3 is comparable to the total flood damages. As
discussed above, this high cost of mitigation and protection actions was not
supported by previous works, although Girons Lopez et al. (2017) used this
parameter.
The SKK model can give a different explanation of the avoidance of false
alarms. Figure 2b shows the relationship between relative loss and
predefined probability thresholds simulated by the SKK model in
Experiment 2 (see Table 4). Although we assumed no cost and an accurate
prediction system (Experiment 2.4; see Table 4), forecasters need to
avoid issuing false alarms by the relatively high predefined probability
thresholds to minimize relative loss (blue line). Due to the cry wolf effect
found in Fig. 1b, forecasters need to decrease the number of false alarms
to mitigate the damage of flooding even if there was no cost of false
alarms. In other words, forecasters in the SKK model need to pay “implicit
cost” of false alarms because false alarms induce not only the cost of
mitigation and protection actions for nothing at the current time, but also
the increase of damages of the future floods by reducing the social
collective trust and preparedness. Considering that the previous works
indicated that the cost of mitigation and protection actions is negligibly
small (i.e., it is realistic to assume η=0), the SKK model reproduces
the relationship between warning thresholds and total losses more
realistically than the GL model. When we degrade the prediction accuracy
(Experiment 2.5; see Table 4), relative loss is more sensitive to
predefined probability thresholds (orange line) because the selection of the
threshold is more important to accurately detect flood events and reduce the
number of false alarms when the prediction is more inaccurate and uncertain.
When we consider the high cost of mitigation and protection actions (Experiment 2.6; see Table 4), small predefined probability thresholds
further increase relative loss (green line).
Figure S2 shows how γ in the Eq. (7) affects the relationship
between relative loss and predefined probability threshold. When the
contribution of social collective trust to social preparedness increases
(i.e., γ gets smaller), the “implicit cost” of false alarms
induced by relatively small predefined probability thresholds increases.
Figure S2 also shows that moderate changes of γ from the default
setting of the SKK model (i.e., 0.5) do not qualitatively change the
relationship between relative loss and predefined probability threshold. In
addition, the qualitative behavior of our SKK model is robust to different
discharge time series (Fig. S3). Figure S3 reveals that the uncertainty
induced by different discharge time series is comparable to that quantified
by 250 Monte Carlo simulations with different initial conditions and
forecast outcomes.
(a–b) The relationship between relative loss and predefined
probability thresholds in (a) the green society and (b) the technological
society. In (a), blue and green lines show the results of Experiments 3.1 and 3.2, respectively. In (b), blue and green lines show the results of
Experiments 3.3 and 3.4, respectively. (c, d) The relationship between
time-averaged social preparedness and predefined probability thresholds in
(c) the green society and (d) the technological society. Black, purple, and
pink lines show time-averaged social preparedness, social collective memory,
and social collective trust in FEWS. Each dot shows the result of the
individual Monte Carlo simulation, and we smoothed them by Gaussian process
regression.
Figure 3a compares the GL and SKK models in the green society. In the
previous Experiments 1 and 2, the damage threshold, δ, is set to
0.35, which is same as Girons Lopez et al. (2017). In Experiments 3.1
and 3.2 (see Table 5), the damage threshold is reduced to 0.20 so that the
number of flood events increases. In this case, the GL and SKK models behave
similarly. Figure 3c shows time-averaged social collective memory, social
collective trust in FEWS, and social preparedness as functions of predefined
probability thresholds. In the green society, frequent flood events make
social collective memory high. In addition, it is easy to maintain the high
social collective trust in FEWS since there are many opportunities to gain
trust when flood frequently occurs. Therefore, both social collective memory
and social collective trust in FEWS are large in the green society. Although
the GL model neglects the social collective trust in FEWS to calculate social
preparedness, the social preparedness of both GL and SKK models is high.
On the other hand, the GL and SKK models work more differently in the
technological society than the green society. The damage threshold, δ, is increased to 0.45 in Experiments 3.3 and 3.4 (see Table 5), so
that the number of flood events is smaller than Girons Lopez et al. (2017).
Figure 3b indicates that the relationship between relative loss and
predefined probability thresholds in the GL model is substantially different
from that in the SKK model. The SKK model produces smaller relative loss
than the GL model when the appropriate predefined probability threshold is
chosen. The sensitivity of relative loss to predefined probability
thresholds is larger in the technological society than the green society.
Figure 3d indicates that it is difficult to maintain the high level of
social collective memory in the technological society, so that considering
social collective trust in FEWS can increase social preparedness. In
addition, the choice of a predefined probability threshold is more important
to maintain the high level of social collective trust in the technological
society than the green society. These behaviors of the models can be found
when damage threshold is further increased to 0.6, although the 1000-year
averaged statistics are strongly affected by random processes due to the
insufficient number of disaster events within the 1000-year computation
period (not shown).
Results of Experiment 4. (a–d) The relationship between
relative loss and predefined probability thresholds in (a) the green society
with accurate forecasts, (b) the green society with inaccurate forecasts,
(c) the technological society with accurate forecasts, and (d) the technological
society with inaccurate forecasts. Increments of trust for true positive,
false negative, and false positive are set to 0.1, 0.1, and 0.1 (blue
lines), 0.1, 0.1, and 0.8 (orange lines), and 0.1, 0.8, and 0.1 (green
lines). See Table 6 for detailed model parameters' settings. (e–h) Same as
(a–d) but for time-averaged social collective trust in FEWS. (i–l) Same as
(a–d) but for threat score (black lines), hit rate (purple lines), and false
alarm ratio (pink lines). Each dot shows the result of individual
Monte Carlo simulation, and we smoothed them by Gaussian process regression.
In Experiment 4, we further analyze the SKK model to discuss the optimal
predefined probability threshold and to provide the useful implication for
the design of FEWS in the various kind of social systems. We have three sets
of parameters in Eq. (9) (see also Table 6). The first set of
parameters is same as Experiments 1–3. Changes in social collective
trust by false negative and false positive are the same (τFN=τFP). In the second set of parameters, we assume social collective trust
substantially decreases by false positive (false alarms) (τFN<τFP): [τTPτFNτFP]=[0.1,0.1,0.8]. In the
third set of parameters, we assume social collective trust substantially
decreases when forecasters miss a flood event (τFN>τFP):
[τTPτFNτFP]=[0.1,0.8,0.1]. The blue, orange,
and green lines in Fig. 4a–d show that the optimal predefined
probability threshold depends on how social collective trust is affected by
false alarms and missed events. When social collective trust is affected by
false alarms more substantially than missed events (orange lines),
forecasters need to have relatively high predefined probability thresholds
to maintain the high level of social collective trust (see Fig. 4e–h) and
minimize relative loss. Figure 4a–d also shows that the differences of
optimal predefined probability thresholds in three sets of parameters become
larger as forecasts become accurate. The optimal predefined thresholds are
bounded by the range in which the high threat scores can be obtained (see
Fig. 4i–l). Thus, more accurate prediction systems make it more
important to change the predefined probability threshold according to the
dynamics of social collective trust. It implies that forecasters need to
prioritize the meteorologically accurate forecasting by maximizing threat
scores. Then, they have room for improvement to change their warning
thresholds based on the dynamics of social collective trust in FEWS.
Discussion and conclusions
In this study, we included the dynamics of social collective trust in FEWS
into the existing socio-hydrological model. By formulating social
preparedness as a function of social collective trust and social
collective memory, we realistically simulate the cry wolf effect in which
many false alarms undermine the credibility of the early warning systems.
Please note that the previous version of the model proposed by Girons Lopez
et al. (2017) cannot do it. Although our model is simple and stylized, we
can provide practically useful implications to improve the design of FEWS.
First, considering the dynamics of social collective trust in FEWS is more
important in the technological society with infrequent flood events than in
the green society with frequent flood events. It implies that weather
agencies need more efforts to be trusted by general citizens to induce their
preparedness actions when a community is more heavily protected by flood protection
infrastructures such as levees and dams. Second, as the natural
scientific skill to predict floods is improved, the efficiency of FEWS gets
more sensitive to the behavior of social collective trust, so that
forecasters need to determine their warning threshold by considering the
social aspects. Considering the recent advances of the skill to predict
extreme hydrometeorological events, it implies that it is becoming more
important for forecasters to take social dynamics responding to weather
forecasts into consideration.
Although our model is the small extension of Girons Lopez et al. (2017), the
implication of our study is completely different from Girons Lopez et al. (2017). Girons Lopez et al. (2017) mainly focused on the influence of the
recency of flood experience on social preparedness and the efficiency of
FEWS. Since their social preparedness is determined only by the flood
experiences and they did not consider social collective trust in FEWS and
weather agencies, the outcome of prediction did not directly influence the
people's behavior in the model of Girons Lopez et al. (2017). By formulating
social preparedness as a function of both social collective memory and
trust, we could evaluate the effects of missed events and false alarms on
preparedness actions. We contributed to connecting the modeling approaches
of system dynamics in socio-hydrology to the existing literature about
complex human behaviors against disaster warnings such as cry wolf effects
in economics, sociology, and psychology (e.g., Simmons and Sutter, 2009;
Ripberger et al., 2015; Trainor et al., 2015; LeClerc and Joslyn, 2015;
Jauernic and van den Broeke, 2017; Lim et al., 2019).
Our findings of the optimal predefined probability thresholds are similar to
Roulston and Smith (2004). Roulston and Smith (2004) developed the simple
model to optimize predefined probability thresholds considering the damage,
cost, and imperfect compliance with forecasting (i.e., the cry wolf effect).
They also revealed that it is necessary to choose high warning thresholds if
intolerance of false alarms of the society is high. However, there are
substantial differences between our study and the previous cost–loss
analysis such as Roulston and Smith (2004). First, Roulston and Smith (2004)
developed the static model in which the cry wolf effect is treated
exogenously, while our model is the dynamic model in which the cry wolf
effect is endogenously simulated. Therefore, our model can consider the
temporal change in the design and accuracy of FEWS, the flood protection
level, and social systems, which may be the significant advantage to analyze
the actual socio-hydrological phenomena. Second, by fully utilizing the
previous achievements of Girons Lopez et al. (2017), we can also consider
social collective memory of past disasters, which is not considered by
Roulston and Smith (2004). This feature of our model can reveal that the
social collective memory also contributes to the optimal predefined
probability thresholds. Similar to Roulston and Smith (2004), our stylized
model has a potential to help forecasters determine the optimal warning
threshold if it can be appropriately calibrated by empirical data.
Our stylized model and findings are consistent with the previous works. In our
model, the subjective perception of warning systems' accuracy controls
social collective trust in a weather agency and preparedness actions, which
is consistent to Ripberger et al. (2015). Our simulation results reveal that
more actual false alarms hamper preparedness actions and induce more
damages, which is consistent to the findings of Simmons and Sutter (2009)
and Trainor et al. (2015). The behavior of the optimal warning threshold is
similar to Roulston and Smith (2004). While the GL model realistically
simulates the behavior of the optimal warning threshold only if
unrealistically high costs of mitigation and protection actions are assumed,
our stylized model needs no costs of mitigation and protection actions to
realistically simulate the behavior of the optimal warning threshold. Our
stylized model is more consistent with the previous works in which the costs
of mitigation and protection actions responding to warnings were found to be
negligibly small (e.g., Schroter et al., 2008; Hallegatte, 2012; Pappenberger
et al., 2015). Our results justify the optimal warning thresholds which
balance false alarms with missed events, and imply that forecasters believe
the existence of cry wolf effects, although it does not necessarily mean
that cry wolf effects exist.
However, the major limitation of this study is that our modeling of social
collective trust is simple and is not fully supported by empirical data. We
assumed that social collective trust in FEWS is affected only by the outcome
of FEWS in our stylized model although there are many other factors which
affect social collective trust in FEWS, such as social activities and
education. Although intuition and theory suggest that many false alarms
reduce the preparedness actions responding to warnings, the existence of the
cry wolf effect in the weather-related disasters is still debatable (see a
comprehensive review of Lim et al., 2019). Simmons and Sutter (2009)
indicated that the recent false alarms negatively impacted the preparedness
actions, so that we modeled the change in social collective trust by the
recent forecast outcome. However, Ripberger et al. (2015) could not find the
statistically significant short-term effect of false alarms, although they
found the statistically significant cry wolf effect using the long-term
data. It should be noted that most of the previous studies related to the cry
wolf effect focused on tornado disasters, and the systematic econometric
analyses have not been implemented for flood disasters, which makes it
difficult to validate our proposed model. The effect of social collective
memory on catastrophic disasters in the actual society is also debatable
(e.g., Fanta et al., 2019). As Mostert (2018) suggested, it is crucially
important to perform case study analyses, obtain empirical data, and
integrate those data into the dynamic model to deepen our understanding of
the hypothesis of the models (e.g., Roobavannan et al., 2017; Ciullo et al., 2017; Barendrecht et al., 2019; Sawada and Hanazaki, 2020).
As discussed above, systematic econometric analyses and field surveys on cry
wolf effects have not been implemented for flood disasters, so it is
important to design such kinds of analyses. Our modeling work provides
useful implications for the design of future field analyses. First, our
results show that the sensitivity of relative loss to predefined probability
threshold is small around its optimal value in many cases. In many field
surveys such as Simmons and Sutter (2009) and Trainor et al. (2015), pairs
of false alarm ratio and damage in many regions of one country are collected
and compared to show the increase of false alarm ratio increases damage.
Assuming that nationwide criteria of issuing warnings are near-optimal, our
study implies that the detectable signal of cry wolf effects in this
approach is weak. Our modeling work implies that it is difficult to quantify
cry wolf effects using time–mean performance of warnings and damages. It may
be the reason why several field surveys contradict with each other, and the
negative effect of false alarm ratio cannot be found in some surveys (Lim et al., 2019). We recommend analyzing the temporal change in behaviors
responding to recent forecast outcomes, although this strategy is costly and
time-consuming. Second, our Experiment 3 implies that it is better to choose
technological societies as a research field because it is more difficult to
distinguish the contributions of experience and trust in less protected
areas.
In socio-hydrology, researchers have mainly focused on the functions of land
use change and water-related infrastructures such as dams, levees, and dikes
in the complex social systems. Although the interactions between social
systems and weather forecasting such as the cry wolf effect are interesting,
the function of FEWS and weather-related disaster forecasting has not been
intensively investigated in socio-hydrology. We call for the new research
regime, socio-meteorology, as the extension of socio-hydrology. In
socio-meteorology, researchers may focus on how social systems interact with
water-related disaster forecasting, how the efficiency of weather
forecasting is affected by other hydrological factors such as land use
and flood protection infrastructures, and how weather forecasting affects
the design of land use and flood protection infrastructures.
Code and data availability
The code to perform the numerical experiments is available in a public
repository (https://gitlab.com/ysawada/sociometeorology, Sawada and Kanai, 2022). This
study does not contain any data.
The supplement related to this article is available online at: https://doi.org/10.5194/hess-26-4265-2022-supplement.
Author contributions
YS, RK, and HK designed the study. YS and RK developed the model and performed the numerical experiments. YS wrote the original draft of the paper. Paper review and editing were performed by YS, RK, and HK.
Competing interests
The contact author has declared that none of the authors has any competing interests.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We used the source code of Girons Lopez et al. (2017), which can be
downloaded at https://github.com/GironsLopez/prep-fews (last access: 14 August 2022).
We thank the two anonymous reviewers for their constructive comments.
Financial support
This research has been supported by the JST FOREST program (grant no. JPMJFR205Q) and the JSPS KAKENHI grant (grant no. 22K18822).
Review statement
This paper was edited by Roberto Greco and reviewed by two anonymous referees.
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