Tide-rainfall flood quotient: an incisive measure of comprehending a region's response to storm-tide and pluvial flooding

The long-term hourly rainfall information (period: 1970–2011) is collected from India Meteorological Department (Pune, India) operated monitoring stations located at Santacruz in Mithi catchment, Paradeep, Bhubaneswar, and Puri in Jagatsinghpur, and Meenambakkam and Nungabakkam in GCC region. The hourly astronomical (period: 1900–2100) and minute-wise observed storm-tide information (period: 2011–2015) are collected from Indian National Centre for Ocean Information Services (Hyderabad, India). The topographic data in the form of bare earth LiDAR DEMs and other geographical information such as river geometry, land-use land-cover, built-up area, and waterbodies corresponding to the most comprehensive data and comprising of the maximum available length i.e. 2011, are obtained from National Remote Sensing Centre (Hyderabad, India).

The design rainfall time-series ($\widehat {\mathbf{R}}$) is computed by employing a novel regionalization technique introduced by Mohanty et al 2018). Here, the rainfall information from the monitoring stations is utilized to form a $\widehat {\mathbf{R}}$ by employing the Depth-Duration-Frequency information and design temporal pattern in a non-linear optimization framework. For the stations, a comprehensive multivariate frequency analysis composing of marginal depth-frequency and marginal-duration frequency is performed using various parametric and non-parametric distributions. More details on the list of distributions/models are provided in Sherly et al (2015) and Mohanty et al (2018). The marginals from these distributions are used to derive the conditional probability using copula functions. The joint return period is derived from the quantile values represented by the reciprocal of exceedance probability as described in the supplementary section (Pseudo Code S1). An elaborate description of this approach is provided in the supplementary section (Text S2: figure S1 is available online at (stacks.iop.org/ERL/15/064029/mmedia)). On the other hand, the design storm-tide time-series ($\widehat {\mathbf{T}}$) is derived by considering astronomical tide and surge (non-tidal residual) elevation modeled with a family of parametric and non-parametric distributions. The quantile values represented by the reciprocal of exceedance probabilities of astronomical tide and surge are used to derive the corresponding design elevations for a particular return period, as described in the supplementary section (Pseudo Code S2). The sum of design astronomical-tide and design surge elevations is considered as design storm-tide elevation. The temporal pattern, obtained by standardizing the observed time series, is multiplied with the design storm-tide elevation to yield the design storm-tide time series. A detailed description of the computation of $\widehat {\mathbf{T}}$ is provided in the supplementary section (Text S3: figure S2).

The flood model simulations are performed by a 1D-2D coupled MIKE FLOOD (MIKE 11 + MIKE 21 FM HD) model (Löwe et al 2017, Jamali et al 2018, DHI 2019). MIKE FLOOD has been preferred in several past studies (Wright et al 2008, Jamali et al 2018, 2019, Abebe et al 2019, Mohanty et al 2020) owing to numerous advantages and unique features over other flood models such as inclusion of a comprehensive hydraulic structures package, GIS integration, consideration of flooding, wetting and drying depths, seamless conversion of high resolution gridded bathymetry to unstructured triangulated mesh for computational simplicity, inland flooding solver for replicating flood wave propagation in steep gradients, and parallel and GPU computing for faster numerical simulations. More details on its scientific background are provided in the supplementary information (Text S4: Sub-section 1, figures S3 to S6). A key highlight of the MIKE FLOOD is the efficiency with which it can account for the interaction between the downstream channel flow and inflowing storm-tide in coastal regions. More details on this interaction, along with the mathematical equations and key assumptions, are provided in the supplementary information (Text S4). The entire landscape (including built-up area) was processed into a non-orthogonal unstructured triangular mesh in a 2D environment, while the river channel bathymetry was modeled in a 1D environment (Text S4: Sub-section 2, figures S7). Both of these interfaces were interlinked to each other in MIKE FLOOD by establishing lateral linkages for each case-study (figure S8). Other flood influencing basin characteristics such as river channel geometry (channel width and depth), overland floodplain slope, and floodplain resistance (land-use and land-cover) are also considered within the flood model. A detailed specification of the various inputs, considered for each case-study is provided in the supplementary information (Text S4: table S2).

A set of validation experiments is carried out to test the performance of the flood model set-up of each case-study under data-scarce situations. For Mithi catchment, a severe flood event of July 2013 is simulated and compared with the observed flood inundation hot-spots. The flood inundation map is able to capture the flood zones, especially the chronic flood inundation locations. Due to the unavailability of any flood maps in Jagatsinghpur district, a 1D water level calibration (September 2011) and validation (August 2004) are performed. The simulated water levels are compared with the observed water levels through four performance indices. The peak water levels are captured accurately, proving the reliability of the model-setup. For the GCC region, the December 2015 flood event is validated by comparing with 407 locations of observed floodwater depths. A high degree of accuracy is achieved during the comparison. After validation, the $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$ time-series in the form of time-varying flow conditions are provided as inputs to the model. Two sets of simulations are designed: (i) Pluvial driven: 24 h $\widehat {\mathbf{R}}$ for 2, 5, 10, 20, 50, 100, 200, 500 and 1000 yr return period with a constant 2 yr return period $\widehat {\mathbf{T}}$ and (ii) Storm-tide driven: 24 h$\,\widehat {\mathbf{T}}$ for 2, 5, 10, 20, 50, 100, 200, 500 and 1000 yr return period with a constant 2 yr return period $\widehat {\mathbf{R}}$. Although infinite combinations of design rainfall and design storm-tide can be constructed, the above proposed simulation schemes (i & ii) are the only means to portray the marginal/individual impacts of the flood-drivers. The flood hazard is quantified based on the tuple of floodwater depth and velocity ['(d,f)'], i.e. the product of depth 'd' and velocity of flood flow 'f', which captures the momentum of floodwater. The hazard is discretized into five classes based on the degree of severity to humans and economic livelihood, as proposed by Mani et al 2014) (table S4). The five classes are: 'very-low' [0 m²s⁻¹ <'(d,f)' ≤ 0.3 m²s⁻¹], 'low' [0.3 m²s⁻¹ <'(d,f)' ≤ 0.7 m²s⁻¹], 'moderate' [0.7 m²s⁻¹ <'(d,f)' ≤ 1.2 m²s⁻¹], 'high' [1.2 m²s⁻¹ <'(d,f)' ≤ 1.6 m²s⁻¹] and 'very-high' ['(d,f)' >1.6 m²s⁻¹] (table S3). We define TRFQ as the ratio of flood inundation extent (FIE) simulated with $\widehat {\mathbf{T}}$ to $\widehat {\mathbf{R}}$ (equation (1)). It is expressed as

$$\begin{equation}{\rm{TRFQ = FI}}{{\rm{E}}_{\widehat {\bf{T}}}}/{\rm{FI}}{{\rm{E}}_{\widehat {\bf{R}}}}\end{equation} \tag{ 1 }$$

We define two variants of TRFQ, namely TRFQ^a, which considers all the five flood hazard classes, and TRFQ^b, which considers only the high and very-high flood hazard classes in their expressions. The contrasting behavior of these TRFQ variants with various sets of pluvial and storm-tide driven simulations is explored for each case-study. However, since very-low, low and moderate flood hazard spots appear more frequently across a region during a flood event unlike the other classes, the consideration of all the flood hazard classes are more likely to skew the TRFQ values. Most importantly, as high and very-high flood hazard classes imply a higher liklihood of damage/loss, be it human, structural, and economic (Middelmann-Fernandes 2010, Jamali et al 2018), TRFQ^b is identified as a more appropriate measure. Based on the TRFQ^b values, we classify the region as storm-tide dominated if TRFQ^b > 1. When TRFQ^b < 1, it refers to pluvial dominated. Later, we investigate if there exists any relation between TRFQ^b and size of catchment. To ensure the flexibility of TRFQ^b on its application to other coastal regions, where different hazard classes might exist, we perform similar experiments and compare the dynamics with two widely used other flood hazard classifications.

The $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$ time-series for the three case-studies are formulated (figure S12). We notice a larger cumulative rainfall depth for all return periods with Mithi (Mumbai), followed by Jagatsinghpur (Orissa) and the GCC (Chennai) region. For instance, with a 100-yr rainfall event, Mithi experiences 541 mm of rainfall, while the latter two regions could accumulate 403 and 359 mm of rainfall. Similar results are noticed in the peak rainfall values as well. The peak rainfall in Mithi and Jagatsinghpur appears at similar and shorter time instances, while in the GCC region, it is slightly delayed. This variation is due to different temporal patterns in these case-studies, which distribute the cumulative rainfall depth at different periods. The harmonic analysis of astronomical tide provides us with 37 tidal constituents, among which the principal diurnal and semidiurnal constituents are tabulated in table S1. These values comply closely with those reported earlier by Unnikrishnan (1999) and Sindhu and Unnikrishnan (2013).

The performance of the flood model for all three case-studies is validated with past flood events. (Text S4; Sub-section: 3). For Mithi catchment, the validation is performed for a 2-day flood event of 23rd and 24th July 2013. We observe a good agreement between the simulated flood areas and the observed inundated regions, especially the high flood-depths are captured properly (figure S9). For Jagatsinghpur district, a 1D water level calibration and validation are performed at two stream-gauge stations located at Naraj and Alipingal with the help of four performance indices. The performance indices are Root Mean Square Error (RMSE), Index of agreement (d), Deviation in peak (D_p), and Percentage deviation in peak (% D_p). The model performs well during calibration and validation, as identified from the performance indices (figure S10 and table S3). The RMSE values were found to be very low [0.24 m and 0.23 m for Naraj and Alipingal in 2011; and 0.26 and 0.24 for Naraj and Alipingal in 2004, respectively] in the two locations during the calibration and validation experiments. The d values closer to unity [0.99 and 0.94 for Naraj and Alipingal in 2011; and 0.99 and 0.98 for Naraj and Alipingal in 2004, respectively] imply an excellent match of the simulated water levels with the observed data. Furthermore, the low values of D_p [0.07 m and − 0.09 m for Naraj in 2011 and 2004; and −0.10 m and −0.17 m for Alipingal in 2011 and 2004] and % D_p [0.25 and −0.83 for Naraj in 2011 and 2004; and −0.82 and −0.78 for Alipingal in 2011 and 2004] indicate that the simulated water level is nearly same as the observed peak water levels of the flood event. For the GCC region, the validation is conducted for a severe flood event that occurred between 1st and 3rd December 2015. Overall, the simulated flood depths match very closely to the observed flood values, except at a few locations over the floodplains of River Adyar. Nearly 60% of the values fall within the range of ±0.5 m, indicating a reasonable degree of accuracy in capturing the observed flood inundation for a complex river network (figure S11).

The flood hazard maps derived with $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$ for Mithi catchment are illustrated in figure 2. We notice a progressive increase of FIE with the escalation of both $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$. However, a comparatively larger FIE is observed with $\widehat {\mathbf{R}}$, which is expected as it covers the entire region, unlike $\widehat {\mathbf{T}}$ whose impact is limited up to a few kilometers from the coastal reaches. With a 200 yr $\widehat {\mathbf{R}}$, we notice a 58% increase in the FIE compared to a 5 yr rainfall event. Similar observations are seen with $\widehat {\mathbf{T}}$ (65% increase). In the case of storm-tide driven flooding, we notice the emergence of inundation along the southern coast. As we focus on the hazard, we find an increase in 'high' and 'very-high areas with an increase in both $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$ elevations but with a subsequent decline in 'very-low' hazard areas. Interestingly, storm-tide dominates rainfall when we quantify the percentage of the area under the aforementioned classes of flood hazard. This observation is dangerous from the viewpoint of human fatalities and damages, as a higher flood hazard is likely to cause more chaos than lower flood hazard. Even with a 200 yr event, as high as 56.15% of the area experiences 'high' and 'very-high' hazard with storm-tide, compared to 39.58% with rainfall. One can easily spot the devastating impact of storm-tide (identified by red and orange), reaching even up to a distance of 7 km from the coastal open boundary. This observation leads to numerous implications for a heavily urbanized city such as Mumbai. The fact that storm-tide impact is prominent to such long distances shall affect the functioning of the urban drainage network. The backflow of seawater blocks the drainage mechanism, thus making it nearly impotent for an efficient flow (Hallegatte et al 2010), which was only one of the major highlights of the devastating July 2005 flood event (944 mm of rainfall in 24 h and 4.48 m of tide). Along with that, the overtopping of sea water in the upstream areas is a menace to the unaccounted slum population (Chatterjee 2010).

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With Jagatsinghpur (figure 3), we notice a massive increase in FIE with the progression of rainfall and storm-tide elevations. When we compare the FIE for a 200 yr $\widehat {\mathbf{R}}$ and $\widehat {\mathbf{T}}$ to the corresponding 5 yr counterpart, we find an increase of as high as 108% and 133%, respectively. With high rainfall depths, several areas in the central region are inundated, which were otherwise facing lower hazard at lesser rainfall depths. The flatness of the terrain in this region is not conducive for easy drainage of floodwater to the Bay of Bengal, consequently progressing the flooding extent and hazard with time. This is why the 'high' and 'very-high' hazard spots continue to increase at higher rainfall elevations. Interestingly, the storm-tide impact is prominent even at lesser design elevations due to the presence of vast intertidal areas and complex network of small streams as they continue to inundate larger areas in the coastal stretches with 'high' and 'very-high' hazard. We find that the areas under 'high' and 'very-high' flood hazard increases steadily (32.01%, 33.17%, 34.47%, and 35.58% with 5-, 50-, 100-, and 200 yr $\widehat {\mathbf{T}}$, respectively), more or less similar to rainfall-driven flooding (48.78%, 53.21%, 55.52%, and 58.58% with 5-, 50-, 100-, and 200 yr $\widehat {\mathbf{R}}$, respectively).

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The flood maps for Chennai are illustrated in figure 4. Similar to Jagatsinghpur and Mithi, higher rainfall and storm-tide events contribute to an increase in FIE than observed with less extreme events. The increment in FIE reaches 107% and 140%, respectively, vis-à-vis a 200 yr and 5 yr $\widehat {\mathbf{R}}$ or $\widehat {\mathbf{T}}$.

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The contribution of rainfall proliferates, especially in the northern and central regions, while the impact of storm-tide is confined to the eastern coastal region, with a majority of them characterized by 'low' hazard. With the rainfall-driven flooding, only a large patch in the southern portion exhibits a 'high' flood hazard, which intensifies with larger rainfall depth. The severe storm-tide impact is almost imperceptible until a 100-yr event, after which the 'high' and 'very-high' hazard areas (10.34%) start appearing; most of these hazard areas confined to the coastal stretches near Adyar, Cooum and Kosasthalyar rivers (northern part). The tidal impact is mostly attenuated by the Buckingham Canal running parallel to the coastline. This finding corroborates that the storm-tide does not largely amplify the severity of flood hazard unless it is a rare extreme event.

The TRFQ^a and TRFQ^b for each region are illustrated in figure 5. In each case, we discover a monotonic progression in the TRFQ values with an increase in the return period. In Mithi (figure 5(a)), the inundation extent with $\widehat {\mathbf{R}}$ exceeds that caused by $\,\widehat {\mathbf{T}}$ as reflected by TRFQ^a values (TRFQ^a < 1). Interestingly, we witness an altogether different behavior while considering 'high' and 'very-high' hazard classes, explained by TRFQ^b. Here, $\,\widehat {\mathbf{T}}$ dominates the $\widehat {\mathbf{R}}$ contribution to flood hazard. This observation is prominent even at low return periods. With a further increase in storm-tide elevation, TRFQ^b increases, signifying a larger contribution to increasing proportions of the area under 'high' and 'very-high' hazard classes. This observation reveals the contrasting features of TRFQ values by the introduction of skew in TRFQ^a with consideration of all flood hazard classes. In Jagatsinghpur (figure 5(b)), both TRFQ^a and TRFQ^b were <1 for all return periods. While considering 'high' and 'very-high' hazard, both the flood drivers contributed nearly equal, but the impact of $\widehat {\mathbf{T}}$ is slightly suppressed. This finding is conclusive from the TRFQ^b values that increase from 0.91 with a 2 yr event and reaches up to 0.95 with a 1000 yr event. In GCC region ((figure 5(c)) $\widehat {\mathbf{R}}$ has a larger impact on inundated areas falling under 'high' and 'very-high' hazard, as a result of which TRFQ^a & TRFQ^b are <1 even at larger return periods.

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4.2.1. Sensitivity of TRFQ (TRFQ^b)