# How to Account for the Human Motion to Improve Flood Risk Assessment in Urban Areas

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## Abstract

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## 1. Introduction

- Pre-emergency evacuation strategies cannot be implemented because of lack of early warnings or Civil Body Protection/First Responders management activities, thus making ineffective coordinated motor vehicles and public transport-based solutions (including, e.g., scenarios in underdeveloped countries);
- Flash flood conditions can exist;
- Flood-affected areas are pedestrian areas and/or the majority of the exposed population is placed outdoors, e.g., along the streets and the public squares;
- The motor vehicle evacuation cannot be performed because of specific conditions, e.g., (a) the urban space configuration (e.g., see compact urban fabric in historical scenarios); (b) critical effects in vehicle use along the evacuation roads, essentially due to vehicle-density related issues, such as traffic jams; (c) prevalence of pedestrian evacuees in respect to motorized ones (e.g., because of socio-economic factors, as for example, in underdeveloped countries);
- Distances to the evacuation areas (or the flood-affected area dimensions) are quite limited, such as in case of shelters in urban areas or “invacuation” strategies (According to PD 25111:2010, this evacuation solution concerns “the movement of people to pre-identified areas inside the building/site in order to protect them from external dangers during an incident”. In flood evacuation, building occupants can remain inside and move towards the higher stories, while individuals placed in the building surrounding try to reach the nearest one and then move upstairs), and they should be reached on foot;
- Disruption of the mobility system can appear as leading people to move on foot;
- The real emergency scenario is quite different from what is expected, thus affecting one of the previous elements;
- Some First Responders activities can imply the movement on foot to support the population in the emergency scenarios.

- Which are the risk-affecting factors in BE, by underlining the population-related contribute (Section 1.1);
- Which tools can be used to merge such two aspects to evaluate the effectiveness of the evacuation (Section 1.2);
- Which models can be used to evaluate man-floodwaters interactions in pedestrian evacuation (Section 1.3).

#### 1.1. BE Risk-Affecting Factors and the Population-Related Contribute

- Location of settlement on floodplains;
- Land use-related issues, by including a lower capacity of absorbing rain by urban surfaces (e.g., low porosity of urban surfaces, especially in high-built up areas) in respect to the ones in rural areas;
- Compact urban areas layout which can increase open-channel related effects in floodwater spreading;
- Insufficient sewer systems, because, e.g., of poor maintenance plans and actions as well as of the variations in functioning conditions (e.g., severity of floods different from the one used in their design) also due to climate-change effects;
- Vulnerability of buildings, suffering damage because of a low resistance level in respect to floodwater strains (e.g., elevations, foundations);
- Low level of control of possible hazard conditions, also in relation to poor flood sensor systems; inadequate management of immediate pre-disaster and disaster conditions, with the possible lack of early warning systems, which can provoke a delay in emergency action starting.

_{f}(m/s) [7,8,9,10,11]. In critical D-V

_{f}conditions, fatalities can be mainly due to: (a) interaction with debris dragged by floodwaters, with the possibility of minor injuries; (b) stability loss (e.g., for pedestrians, they can be due to possible buoyancy or body failure/dragging phenomena), with the consequent possibility of drowning and death. Similar problems can be related to both people moving on foot or by (motor) vehicles [7,8].

- Emergency planning elements: poor awareness/preparedness levels of the population can bring people to adopt risky behaviors, underestimate the impact of disasters conditions, and delay the starting of safety procedures. Meanwhile, a similar result can be provoked by ineffective early warning systems. Emergency plans can be not well known by the population, hence making impossible to properly identify “safe” areas and gathering points, as well as evacuation paths;
- Surrounding BE elements: people generally try to move towards the nearest areas with lower floodwaters depth and speed (e.g., ground elevations), by looking for direct support of unmovable obstacles to move in floodwaters (e.g., fences, street furniture). Meanwhile, they try to modify their motion direction to avoid all the obstacles dragged by the flood (e.g., cars, debris);
- Other individuals and belongings: social share identity (including phenomena connected to information exchange) and attachment-to-things effects are time-wasting behaviors that can delay or slow down the evacuation process. Such elements can also bring people to move towards “unsafe” areas (e.g., to rescue other individuals, to retrieve some personal belongings, or to guard the properties). People can also prefer to move in a group by sharing evacuation direction and motion speed;
- Floodwaters: “curiosity” effects lead individuals to delay the evacuation starting to observe floodwaters conditions or event recording with smartphones or cameras. Meanwhile, when floodwaters depth and speed increase, the possibility to freely move is reduced and the evacuees’ motion process is slowed down, hence increasing the overall evacuation time.

#### 1.2. Simulation Tools to Risk-Assessment and Risk-Mitigation Strategies Evaluation

#### 1.3. Modelling Pedestrians’ Evacuation in Floodwater: Current Approaches and Limitations

_{i}(m/s) have been recently performed through real-world event analysis [10] or laboratory experiments in open channels [33,44] or pools [42]. Nevertheless, only a limited number of works succeeds in overlaying the main constraints due to [33,36,42]: (a) the limited number of individuals, also in relation to the different age classes; (b) the effects of individuals’ excitement conditions (i.e., walking versus running).

## 2. Phases, Materials, and Methods

- General characterization of the selected database, according to Section 2.2 methods. The motion speeds in walking and running conditions are compared depending on D and on the individuals’ gender. In this way, it can be possible to respectively trace general relationships depending on floodwater-characterization constraints to motion and to individuals’ main features;
- Modelling of the speed variation (normalized speed and dimensional speed variations) depending on D and in respect of the dry surface motion, according to Section 2.3 methods. In particular, dry surface motion speeds are retrieved according to average literature values depending on the age [43]. The individuals’ height (i.e., the knee height from the ground) is considered in the model because of the related influence assessed by preliminary works on motion and human body stability conditions in floodwaters [9,44];
- Modelling of the normalized speed variation depending on D in respect to the minimum constraint and maximum excitement conditions for the considered database, according to methods in Section 2.4. Such model delves into specific experimental conditions and sample features, to generalize speed estimation data regardless of dry surface motion conditions data.

#### 2.1. Materials: Original Input Database Characterization

_{f}= 0 m/s) to better focus on the effects of depth on v

_{i}. For each individual involved in the test, the original database includes: (a) the motion speeds v

_{i}(m/s) referred to the specific tested floodwaters and excitement conditions; (b) the individuals’ features (i.e., sex, gender, height, mass, body mass index); (c) the number of performed tests. Each individual performed the test once in walking and running conditions, for a given D, and 31 individuals performed the test for all the D values.

#### 2.2. General Methods for Model Definition and Characterization of the Selected Database

_{w,exp}-v

_{r,exp}(m/s) pairs analysis depending on:

- Gender, to evaluate difference among the two excitement conditions and compare them with previous works outcomes (i.e., males generally moves faster than females) [43].

^{2}values to focus on the direct correlation between the two assessed variables. Then, simple models to be integrated into simulators can be traced. According to previous works on the original database [44], all the models have been evaluated through the Bisquare regression method, which allows finding the regression that fits the bulk of the data and minimizes the effect of outliers.

_{w,ex}= v

_{r,exp}line (no differences between walking and running conditions) is shown to confirm if the above regressions are over this ratio.

#### 2.3. Methods for Speed Variation Modelling Depending on D and Dry Surface Motion Conditions

_{i}(m/s) and D in absolute terms (m/s) [33,34,44], but only a limited number of works tried to define such correlations in respect of free-flowing and dry surface motion conditions [33], that is, the no-constraint conditions for human body motion also in evacuation conditions. The use of such normalized speed could instead improve the generalization of simulation models by allowing to overlap normalized speed variations and the main motion-affecting individuals’ parameters (e.g., age, gender) [43,46]. Thus, this second approach has been followed, and the individuals’ speeds v

_{i}(m/s) have been expressed in relation to maximum or ideal evacuation speeds and so in non-dimensional terms (-).

_{id,a}, according to the curve a [46] (see Figure 1a) and v

_{id,b}, according to the curve b [43] (see Figure 1b). These two curves offer different age-related values, and in particular, the curve b [43] can be selected to consider precautionary conditions in normal motion since it generally offers speed values lower than the one of the curve a [46].

_{a,r}and v*

_{b,r}) and walking (v*

_{a,w}and v*

_{b,w}) conditions:

_{a,r}= v

_{r,exp}/v

_{id,a}, v*

_{b,r}= v

_{r,exp}/v

_{id,b}, v*

_{a,w}= v

_{w,exp}/v

_{id,a}, v*

_{b,w}= v

_{w,exp}/v

_{id,b}

- Variation of the normalized speed v* in respect of D experimental classes: the distribution of v* in respect of D experimental classes takes advantages of boxplot analysis and graph to evidence if and how the input data are widespread and if outliers are present. Input data involve the whole sample and male (outlined by subscript M) and female (outlined by subscript F) separate samples to highlight the differences due to gender. In general terms, it is expected that running regression model should involve higher v* values, especially for lower D-related input data;
- Variation of the normalized speed v* in respect of K-D: linear regression models are tested. Such modelling approach allows detecting the effects of the reciprocal position of knee and floodwater levels. Male and female samples are shown in the regression model but considered together in the regression model to focus on the main factor influencing human behavior, which is the individuals’ height. It is expected that v* should be equal to or higher than 1 when the knee is placed outside the floodwaters, especially in running conditions.

#### 2.4. Methods for Normalized Speed Variation Modelling Depending on D, Minimum Constraint, and Maximum Excitement Conditions for the Considered Database

_{i,r,0.2}= v

_{r,exp}/v

_{r,0.2}, v

_{i,w,0.2}= v

_{w,exp}/v

_{r,0.2}

_{r,}

_{0.2}(m/s) is the individuals’ running speed for D = 0.2 m. For this reason, all the v

_{i,r,}

_{0.2}for D = 0.2 m will be equal to 1. The distribution of v

_{i,r,}

_{0.2}(cm) in respect to D tested values is assessed and shown by a boxplot comparison. Linear regression is provided to evidence the general trend of the sample for separated running and walking excitement conditions. Due to the smaller sample dimension, it is assumed that the regressions are evaluated by collecting males and females in a unique sample.

_{i,r,max}and walking v

_{i,w,max}excitement conditions:

_{i,r,max}= v

_{r,exp}/v

_{r,ma}, v

_{i,w,max}= v

_{w,exp}/v

_{w,max}

_{r,max}and v

_{w,max}are respectively the maximum running and maximum walking speed. This normalization procedure allows to consider the effective D value for which the individual had the maximum motion speed. Hence, the boxplot distribution representation can have v

_{i,r,max}and v

_{i,w,max}values equal to 1 also for D > 0.2 m.

## 3. Results

#### 3.1. Characterization of the Selected Database

^{2}values show a moderate correlation trend for both the gender-related sample.

^{2}values for the regression models). D equal to 0.4 m and 0.5 m evidences small differences in regression trends (5% in respect of D = 0.5 m) because the related sample is composed by individuals with knees outside and inside the floodwater level, also according to Figure 2 results. Meanwhile, D equal to 0.5 m and 0.6 m seems to additionally provoke the same conditions in v

_{w,exp}and v

_{r,exp}pairs, confirming previous works outcomes [44]. In such conditions, the knee and a part of the above leg are generally placed inside the water, by involving a similar physiological and kinematic constraint in human body motion.

#### 3.2. Speed Variation Modelling Depending on D and Dry Surface Motion Conditions

- Motion speed (and so v*) decreases while D increases. Regressions on the curve a-based model show a slighter regression slope, according to the first term in the regression equation (−8% for running conditions and −16% for walking conditions in respect to the curve a-based model). Hence, curve b-based models seem to amplify the v* reduction;
- The speed-D relationship in both the excitement conditions can be properly represented by using speed normalization. In particular, regressions on the curve a [46]-based model show a moderate relationship, according to the R
^{2}value, for both walking and running conditions. R^{2}values for the curve b [43]-based model are lower than these, suggesting that this model more limitedly represents the effects of D in v* variation. Hence, the adoption of curve a-based model could improve the prediction model capabilities in evacuation simulators; - In view of the above, differences between running and walking excitement conditions exist. In particular, the effects of D on the variation of speed in walking conditions seem to be less relevant than the ones of running conditions. This result is evidenced by the more significant presence of possible outliers (see Figure 6) and by the lower value of the first coefficient of the linear regression (about −70% in respect to running conditions model). This result confirms the original work outcomes [44] and the outcomes of studies concerning other evacuation typologies [47]. In fact, issues related to the individual’s motion effort and the distance between individual and motion goals seem to be more relevant while people are running towards the motion goal (as in evacuation conditions). In addition, it is worth noting that the assessed v* value in the dry surface for running conditions is about 2 times greater than the one for walking conditions, regardless of the adopted model. Besides, v* in running conditions seems to be equal to about 1 when D is about 0.3 to 0.5m, which corresponds to the D classes for which the individuals’ knee is generally closer to the floodwater level, according to Figure 2 statistics;
- Differences between dry surface motion in literature reference works [43,46] and the adopted database [44] exist (compare the second linear regression coefficient in all the models), by underlining how specific database should be adopted to represent the flood evacuation. Forecasted v* for D < 0.2 m are beyond the lower limit of the tested D conditions and so they could be affected by additional non-linear speed-D interferences [33]. Nevertheless, the importance of this result is shown by the v* values for the minimum tested constraint conditions (D = 0.2 m) in both walking and running conditions.

- Males seem to move faster than females in running conditions, confirming previous works outcomes [33,43] and Section 3.1 (i.e., compare with Figure 3) outcomes. This result is evidenced by the second linear regression coefficient in both the models (in curve a-based model: 1.33 for males versus 1.23 for females; in curve b-based model: 1.47 for males versus 1.36 for females). In particular, males seem to move +8% faster (in normalized terms) in dry surface conditions, in both models;

^{2}generally higher also for curve b-based model). All these results confirm the importance of floodwater-knee interaction as the main behavioral driver for the whole sample [44].

^{2}values (<0.25) for “average” age-v regression line (due to the original database pairs dispersion). Nevertheless, they generally confirm the previous modelling outcomes as well as the results of previous works. Firstly, the general trend of 4th polynomial regression is confirmed in each excitement conditions, by underlining that elderly’s speeds are lower than the one of adult individuals. In addition, it could be evidenced that:

- Considering running conditions, the age-v regression for the overall sample is over the references curves when D ranges from 0.2 m to 0.4 m, regardless of the considered curve in the model; this result confirms the “average” results of Figure 9. Meanwhile, the regression curves on the maximum age-v pairs seem to be always over the reference curves or, at least, equal (i.e., if considering the curve b data);
- On the contrary, walking conditions-related regression on maximum age-v pairs are generally under the reference curves, with similar predicted values for the age range 10 to 30 years. This seems to evidence that younger individuals can generally be less affected in their motion by D conditions, confirming previous results on age-related impact on motion speed [42,43,44]. Average age-v pairs regression in walking speeds seems to evidence no substantial differences, especially for intermediate ranges, confirming the interpretation of outcomes in Figure 6 and Figure 10.

#### 3.3. Normalized Speed Variation Modelling Depending on D, Minimum Constraint, and Maximum Excitement Conditions for the Considered Database

_{r,}

_{0.2}(hence, all the values are equal to 1), but the maximum v

_{i,r,}

_{0.2}values decrease while D increases. In addition, the median linear regression denotes a moderate relationship between D and v

_{i,r,}

_{0.2}, as shown by the R

^{2}value. On the contrary, walking conditions-related speeds v

_{i,w,}

_{0.2}seems to be less influenced by D, as demonstrated by the scattered boxplot values distribution and by the inconsistent R

^{2}value.

^{2}values, it is demonstrated that:

_{i,r,max}values are linked to the lowest D values, while walking conditions see a more widespread v

_{i,w,max}distribution. This outcome evidences the existence of excitement-related issues (i.e., motion effort increasing with constraints increase) in pseudo-evacuation excitement conditions, in respect to normal excitement conditions (pseudo-evacuation conditions can be approximated by running test, while normal conditions by walking tests) [44,47].

- The effect of D on an individual’s speed is higher while the pedestrian is moving with the knee outside of the floodwater level, especially in running conditions as shown for the sub-sample with the knee inside the floodwater by: (a) the lower R
^{2}value, (b) the wider range for boundary conditions (99%) regression lines, and (c) the lower first regression coefficient value (only for running conditions of Figure 16).

## 4. Results Discussion in View of Model Implementation in Flood Evacuation Simulators

- Effects due to the presence of other pedestrians: crowd-density effects could reduce the speeds in compact groups; social shared identity factors could lead people to share the same direction and to adjust their individual speeds to remain in group (e.g., waiting for more vulnerable and slow group members);
- Guidance and support elements: they can speed up the process by giving continuous support to the evacuee in terms of direction to be followed and in terms of physical aid (e.g., handrails along the paths);
- Other flood-related phenomena like the attraction towards unmovable obstacles, according to the aforementioned support needs of the evacuees.

- Input running conditions used in this study are similar to the one of excited individual, who, for instance, participate to an evacuation process with a high engagement level (e.g., because of rising floodwater levels or other hazard-increasing evacuation drivers perceived by the individuals);
- Input walking conditions used in this study are similar to the one of normal motion individual, who for instance, participate in an evacuation process in still waters, or under organized circumstances.

- Dimensional models, which are the ones in which the dependent variables are directly expressed in dimensional terms (i.e., the dependent variable is a speed (m/s) (Table 1). These models allow tracing the simplest solutions to predict motion speed in flood evacuation according to a microscopic approach, by directly retrieving evacuation speed values in dimensional terms (m/s) only according to a single motion driver [41,43];
- Normalized models, which are the ones in which the dependent variables are a non-dimensional parameter v
_{norm}(-) (Table 2). To calculate the effective motion speed, v_{norm}should be multiplied by the isolated individuals’ speed, which can be the one in (a) minimum constraint-maximum excitement conditions in the tested database (v_{r,}_{0.2}) or (b) dry surface motion (v_{id}). Although the validity of the model application can be extended to different isolated pedestrians’ speed databases, the use of reference curves by this work for models development is encouraged especially in the second aforementioned case (i.e., [46], and so to v_{id,a}, due to the higher statistical significance of results).

## 5. Conclusions and Future Research Remarks

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 2.**Database characterization depending on K-D versus the tested D values. The boxplot graph includes possible outliers (shown by “+”). The linear regression and the 99% boundaries are shown.

**Figure 3.**Database characterization depending on v

_{w,exp}and v

_{r,exp}pairs, for each individual, by distinguishing females (continuous red line) and males (dashed blue line) linear regressions and related samples.

**Figure 4.**Database characterization depending on v

_{w,exp}and v

_{r,exp}pairs, for each individual, by distinguishing the linear regressions for each of the tested D. The regression equations are shown as a function of the respective v

_{w,exp}for the considered D value (subscript expressed in (cm)).

**Figure 5.**Normalized speed variation for running conditions depending on D in respect to dry surface motion conditions, for the whole sample (male and female together): (

**a**) according to the curve a [46]; (

**b**) according to the curve b [43]. Linear regressions (dashed lines refer to prevised values outside of the tested D range) and boundary conditions (99%) are shown. Outliers are shown in the boxplot representation (marked by “+”).

**Figure 6.**Normalized speed variation for walking conditions depending on D in respect to dry surface motion conditions, for the whole sample (male and female together): (

**a**) according to the curve a [46]; (

**b**) according to the curve b [43]. Linear regressions (dashed lines refer to prevised values outside of the tested D range) and boundary conditions (99%) are shown. Outliers are shown in the boxplot representation (marked by “+”).

**Figure 7.**Normalized speed variation depending on D in respect to dry surface motion conditions, for the male sample: (

**a**) for running conditions, according to the curve a [46]; (

**b**) for running conditions, according to the curve b [43]; (

**c**) for walking conditions, according to the curve a [46]; (

**d**) for walking conditions, according to the curve b [43]. Linear regressions (dashed lines refer to expected values outside of the tested D range) and boundary conditions (99%) are shown. Outliers are shown in the boxplot representation (marked by “+”).

**Figure 8.**Normalized speed variation depending on D in respect to dry surface motion conditions, for the female sample: (

**a**) for running conditions, according to the curve a [46]; (

**b**) for running conditions, according to the curve b [43]; (

**c**) for walking conditions, according to the curve a [46]; (

**d**) for walking conditions, according to the curve b [43]. Linear regressions (dashed lines refer to expected values outside of the tested D range) and boundary conditions (99%) are shown. Outliers are shown in the boxplot representation (marked by “+”).

**Figure 9.**Normalized speed variation for running conditions depending on K-D in respect to dry surface motion conditions, for the whole sample (male and female together): (

**a**) according to the curve a [46]; (

**b**) according to the curve b [43]. Linear regressions (dashed lines refer to expected values outside of the tested D range) and boundary conditions (99%) are shown. Male and female samples experimental pairs are shown.

**Figure 10.**Normalized speed variation for walking conditions depending on K-D in respect to dry surface motion conditions, for the whole sample (male and female together): (

**a**) according to the curve a [46]; (

**b**) according to the curve b [43]. Linear regressions (dashed lines refer to expected values outside of the tested D range) and boundary conditions (99%) are shown. Male and female samples experimental pairs are shown.

**Figure 11.**Average dimensional age-evacuation speed (m/s) model in running conditions, for the different D values according to a polynomial (4th degree) regression model, performed on all the experimental pairs (male and female together): (

**a**) compared to the curve a [46]; (

**b**) compared to the curve b [43].

**Figure 12.**Average dimensional age-evacuation speed (m/s) model in walking conditions, for the different D values according to a polynomial (4th degree) regression model, performed on all the experimental pairs (male and female together): (

**a**) compared to the curve a [46]; (

**b**) compared to the curve b [43].

**Figure 13.**Maximum dimensional age-evacuation speed (m/s) model in running conditions, for the different D values according to a polynomial (4th degree) regression model, performed on all the experimental pairs (male and female together): (

**a**) compared to the curve a [46]; (

**b**) compared to the curve b [43].

**Figure 14.**Average dimensional age-evacuation speed (m/s) model in walking conditions, for the different D values according to a polynomial (4

^{th}degree) regression model, performed on all the experimental pairs (male and female together): (

**a**) compared to the curve a [46]; (

**b**) compared to the curve b [43].

**Figure 15.**Normalized speed variation depending on D, by normalizing the speed values by v

_{r,}

_{0.2}(speed of the individual in minimum constraint and maximum excitement conditions within the tested D range): (

**a**) for running conditions; (

**b**) for walking conditions. Linear regressions (dashed lines refer to prevised values outside of the tested D range) and boundary conditions (99%) are shown.

**Figure 16.**Effects of knee position (outside and inside the floodwater level) on the normalized speed variation depending on D, by normalizing the speed values by v

_{r,max}. The regressions are shown for running conditions. Linear regressions (dashed lines refer to prevised values outside of the tested D range) and boundary conditions (99%) are shown.

**Figure 17.**Effects of knee position (outside and inside the floodwater level) on the normalized speed variation depending on D, by normalizing the speed values by v

_{w,max}. The regressions are shown for walking conditions. Linear regressions (dashed lines refer to prevised values outside of the tested D range) and boundary conditions (99%) are shown.

Independent Variables (unit of measure) | Dependent Variable (unit of measure) | Regression Model (sample) ^{1,2} | R^{2 1} | Specific Discussion |
---|---|---|---|---|

walking speed v_{w,exp} (m/s); gender (F or M) | running speed v_{r,exp} (m/s) | v_{r,exp} = 1.6v_{w,exp} (F)v _{r,exp} = 1.76v_{w,exp} (M) | ≈0.5 | Figure 3, Section 3.1 |

walking speed v_{w,exp} (m/s); floodwater depth D (m) | running speed v_{r,exp} (m/s) | D = 0.2 m: v_{r,exp} = 1.89v_{w,exp} (A)D = 0.3 m: v _{r,exp} = 1.83v_{w,exp} (A)D = 0.4 m: v _{r,exp} = 1.67v_{w,exp} (A)D = 0.5 m, 0.6 m: v _{r,exp} = 1.56v_{w,exp} (A)D = 0.7 m: v _{r,exp} = 1.48v_{w,exp} (A) | ≈0.5 | Figure 4, Section 3.1 |

age (years) | “maximum” running speed v_{r,exp} (m/s) | 4th polynomial regression model graphically traced in Figure 13 | >0.7 | Figure 13, Section 3.2 |

age (years) | “maximum” walking speed v_{r,exp} (m/s) | 4th polynomial regression model graphically traced in Figure 14 | >0.7 | Figure 14, Section 3.2 |

^{1}Coefficients are valid for the considered sample; further activities should be performed to check their validity.

^{2}F refers to female sample, M refers to male sample, A refers to both male and female samples together.

**Table 2.**Selected modelling approaches based on non-dimensional dependent variables. In the regression model column, the expression inside round brackets is v

_{norm}.

Independent Variables (Unit of Measure) | Dependent Variable (Unit of Measure) | v_{norm} Regression Model (Sample) ^{1,2} | R^{2 1} | Specific Discussion |
---|---|---|---|---|

floodwater depth D (m) | running speed v_{r} (m/s) | v_{r} = (−0.85D + 1.28)v_{id,a} (A) | ≈0.5 | Figure 5a, Section 3.2 |

floodwater depth D (m) | walking speed v_{w} (m/s) | v_{w} = (−0.25D + 0.64)v_{id,a} (A) | ≈0.6 | Figure 6a, Section 3.2 |

floodwater depth D (m); gender (F or M) | running speed v_{r} (m/s) | v_{r} = (−0.86D + 1.23)v_{id,a} (F)v _{r} = (−0.86D + 1.33)v_{id,a} (F) | >0.5 | Figure 7a and Figure 8a, Section 3.2 |

relative position between the knee height and the floodwater level K-D (m) | running speed v_{r} (m/s) | v_{r} = (−0.86D + 0.86)v_{id,a} (A) | ≈0.6 | Figure 9a, Section 3.2 |

relative position between the knee height and the floodwater level K-D (m) | walking speed v_{w} (m/s) | v_{w} = (−0.25D + 0.51)v_{id,a} (A) | ≈0.6 | Figure 10a, Section 3.2 |

floodwater depth D (m) | running speed ^{3} v_{r} (m/s) | v_{r} = (−0.73D + 1.14)v_{r,}_{0.2} (A) | ≈0.4 | Figure 15a, Section 3.3 |

^{1}Coefficients are valid for the considered sample; further activities should be performed to check their validity.

^{2}F refers to female sample, M refers to male sample, A refers to both male and female samples together.

^{3}This model considers the original database-related speed and not the reference curve as the multiplication value of v

_{norm}.

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**MDPI and ACS Style**

Bernardini, G.; Quagliarini, E.
How to Account for the Human Motion to Improve Flood Risk Assessment in Urban Areas. *Water* **2020**, *12*, 1316.
https://doi.org/10.3390/w12051316

**AMA Style**

Bernardini G, Quagliarini E.
How to Account for the Human Motion to Improve Flood Risk Assessment in Urban Areas. *Water*. 2020; 12(5):1316.
https://doi.org/10.3390/w12051316

**Chicago/Turabian Style**

Bernardini, Gabriele, and Enrico Quagliarini.
2020. "How to Account for the Human Motion to Improve Flood Risk Assessment in Urban Areas" *Water* 12, no. 5: 1316.
https://doi.org/10.3390/w12051316