Assessment of climate change impact on probable maximum floods in a tropical catchment

The increases in extreme rainfall could increase the probable maximum flood (PMF) and pose a severe threat to the critical hydraulic infrastructure such as dams and flood protection structures. This study is conducted to assess the impact of climate change on PMF in a tropical catchment. Climate and inflow data of the Tenmengor reservoir, located in the state of Perak in Malaysia, have been used to calibrate and validate the hydrological model. The projected rainfall from regional climate model is used to generate probable maximum precipitation (PMP) for future periods. A hydrological model was used to simulate PMF from PMP estimated for the historical and two future periods, early (2031 − 2045) and late (2060 − 2075). The results revealed good performance of the hydrological model with Nash–Sutcliffe efficiency, 0.74, and the relative standard error, 0.51, during validation. The estimated rainfall depths were 89.5 mm, 106.3 mm, and 143.3 mm, respectively, for 5, 10, and 50 years of the return period. The study indicated an increase in PMP by 162% to 507% and 259% to 487% during early and late periods for different return periods ranging from 5 to 1000 years. This would cause an increase in PMF by 48.9% and 122.6% during early and late periods. A large increase in PMF indicates the possibility of devastating floods in the future in his tropical catchment due to climate change.


Introduction
Globally, floods share about 40% of total damage due to natural disasters (Noji 1991). The frequency and severity of floods are more in a tropical region, and therefore, most of the damages due to floods are observed in tropical countries (Ohl and Tapsell 2000;Pour et al. 2020a). The majority of the tropical region receives a high amount of rainfall, which also varies with large-scale ocean-atmospheric cycles like other regions. However, the spatiotemporal rainfall variability in tropical areas is more affected by southern oscillation and Atlantic multi-decadal oscillation, which causes high rainfall in some seasons (Goly and Teegavarapu 2013;Pour et al. 2020c(. In El-Nina years, high rainfall often occurs as several extreme rainfall episodes that cause divesting floods (Muhammad et al. 2019).
Floods in most parts of the world have been projected to increase due to the increase in rainfall extremes driven by global warming-induced climate change (Change 2014;Vitousek et al. 2017;Tabari 2020(. Therefore, several studies investigated floods considering climate change impact (Chao et al. 2019;Jennifer and Agnieszka 2020;Wasko et al. 2020;Sharafati and Pezeshki 2020;Sharafati et al. 2021). Rainfall extremes in tropical regions are highly sensitive to global warming. It has been estimated that a 1 °C rise in temperature would cause 10% heavier rainfall extremes in tropical regions. Therefore, the probability of flooding is higher in the tropics than in other parts of the world (Vitousek et al. 2017(. Increased rainfall extremes will increase the severity of floods, which may severely affect the economy and livelihood in tropical regions. The flood occurs due to probable maximum precipitation (PMP) under the most favorable catchment hydraulic condition (e.g., maximum moisture) that is known as probable maximum floods (PMF). The PMP and PMF are essential for designing hydraulic structures to mitigate the effect of floods. It can be anticipated that increased rainfall extremes in tropical regions due to climate change will certainly increase PMP and PMF (Beven 2012;Rientjes et al. 2013). Such information is important for designing or retrofitting hydraulic structures to adapt and mitigate climate change. A general procedure for estimating PMF is the PMP estimation by fitting distribution to extreme rainfall for different return periods and then used in a rainfall-runoff simulation model to generate PMF (Beven 2012).
Rainfall-runoff (R-R) models link rainfall (precipitation) with the watershed's runoff. Identifying the runoff from the rainfall events is required for investigating the forecasting of the streamflow from rainfall (Smith 1965). Such forecasts are important for deciding design factors of hydraulic infrastructures, early warnings for future floods or droughts, operating of reservoir or hydropower plants, and planning irrigation and water resources management activities (Bakhtiari 2018;Ferraro, et al. 2020;Li et al. 2020;Ren et al. 2020;Yang et al. 2020). The relationship between rainfall and runoff is always complicated to define because of the immense spatial and temporal variability of rainfall, and the physical characteristics of the watershed, as well as a few hydrological features of the watershed, need to consider for modeling (Choi et al. 2020;Gan et al. 2020;Ling et al. 2019). Therefore, many R-R models have been developed over time based on a different concept (Kimura et al. 2019;Sajadi et al. 2020). The existing R-R models could be categorized into three main classes, empirical, conceptual and physical. Physically based R-R models represent the "physics" behind the catchment hydrological processes that generate runoff. Generally, these models employed the partial differential equations (PDE) to propose an appropriate understanding of the catchment's R-R interrelationship and process (Ciupak et al. 2019;Velázquez-Zapata 2019). The model parameters and variables should be closely related to or identical with actual characteristics of the catchment hydrological system for the physicalbased model. Thus, physically based models can represent the catchment's hydrologic state at any time. Usually, these models are developed based on two or three-dimensional concepts, and hence, the required data to adequately develop the model is considerably huge compared with other model types. On the other hand, for the empirical models, the required data is the meteorological, physiography, and the geology features at several locations along with the watershed (Farzin et al. 2018). Furthermore, for the mathematical identification of boundary condition, additional information about the nature and type of the catchment boundary conditions are necessary to be available (Rientjes et al. 2013).
A conceptual model is considered when relatively simple mathematical relations best represent a system's physics (Artificial Neural Networks in Hydrology. I: Preliminary Concepts, 2000). The main idea of conceptual models is that discharge has a relationship with storage through some transformation equations and conservation of mass equations (Rientjes et al. 2013). There are a few numbers of conceptual models procedures to consider the representations for the parameters and the variables to mimic the temporal and spatial distribution within the catchment. In this context, these model types used a simplified procedure as the one used in the physical-based model concept, while the others used the lumped concept, which is used in the empirical modeling concept. The existing literature indicates the conceptual model as the most widely used one. The conceptual modeling procedure can also be referred to as grey-box models since they consider a hybridization of the empirical (black box) and physically based (white box) models.
R-R models can be implemented completely within an analytical framework based on input and output observations of catchment water flow. The study area catchment could be considered Black-Box packaging of features. Hence, there is no need to pay attention to the inner hydrological or meteorological process to detect the interrelationship between the rainfall and the runoff (Beven 2012). These models are also called empirical models and are often recommended when the relationship between rainfall and runoff becomes difficult to describe with a limited amount of available data. Therefore, empirical models are often used for the catchment, where the availability of hydrological data and information is very limited. However, empirical models have several drawbacks that restrict their suitability. The Black-Box model's parameters (e.g., regression Coefficient) are derived from the catchment's historical data. Thus, the model could only be used for the particular catchment. Besides, the validation of the model will remain only for the used time-period used for developing the model. Therefore, deciding the suitable model to build the RR model for a catchment is challenging for hydrologists. Several advantages could be noticed when the conceptual models are used, such as the straightforward procedure, easy implementation, and better simulation (Víctor et al. 20,180). The conceptual hydrological models can also support the decision-making processes related to management. They could be used to simulate the impact of climate change on hydropower generation (Chilkoti et al. 2017) and hydrological modeling in the ungauged catchment (Ibrahim et al. 2015) and evaluate the effects of wildfires and land-use changes (Moussoulis et al. 2015;Younis and Ammar 2017). Based on the above, the conceptual hydrological (Mike NAM) model was used in the study. The Mike Nam model has been widely adopted in different catchments having varying climate conditions (Madsen 2000).
The objective of the present study is to assess the impacts of climate change on PMF in a tropical catchment located in Peninsular Malaysia. A physically based hydrological model known as Mike NAM was used to simulate extreme runoff due to extreme rainfall. The PMP for historical (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) and two future periods (2031 − 2045 and 2060 − 2075) was estimated through probability distribution fitting of observed and regional climate model projected rainfall, respectively. The impact of climate change on hydrological extremes at regional and local scales is vital to assess since these alterations are not uniform over the globe. It is expected that the information about possible impacts of climate change on PMF generated in this study would help in decision-making in the planning and development of flood mitigation hydraulic structures.

Study area
Perak River is the second largest river in Peninsular Malaysia. It has an approximate length of 427 km and a catchment area of 15,180 km2, covering about 71% of the Perak state. The origin of the river is located in the mountains of the north Perak 2,000 m above mean sea level. It flows southward from the origin and finally discharges to the Straits of Malacca in Bagan Datoh. Four hydropower dams were constructed along the upper Perak river basin at Temenggor, Bersia, Kenering, and Chenderoh, known as Perak River hydroelectric scheme. A catchment area of 3506 km 2 feeds the Temengor reservoir. The elevation at the catchment area ranges from 206 to 2156 m. The catchment is mostly forested and consists of a lake with a surface area of about 150 km 2 known as Temengor lake. Figure 1 shows the location of the Temengor catchment on the map of Peninsular Malaysia.

Data acquisition
Rainfall and evaporation data are essential for modeling any hydrological processes. Daily rainfall data from eight rain gauges located within the Temengor catchment were used. There are no evapotranspiration measuring stations within the Temengor reservoir catchment area. Therefore, the evapotranspiration measuring station nearest to the study area (STN. PETAK UJIAN) was used. Figure 2 shows the locations of rainfall gauges in the catchment. The details of each station are given in Table 1. The time series of rainfall data at different catchment locations are presented in Fig. 2. Rainfall data are collected from the Department of Irrigation and Drainage (DID), Malaysia, and the evapotranspiration data is collected Malaysian Meteorological Department. Temengor reservoir daily inflow data for the period 2007-2014 was used to calibrate and validate the model. Inflow data was collected from the Tenaga Nasional Berhad (TNB), Malaysia. Many streamflow and water level gauging stations are distributed along Perak River, but most of the data collected from these stations were incomplete. Therefore, reservoir inflow data is used to calibrate and validate the hydrological model. The geospatial data, such as the digital elevation model (DEM) for the study area, is acquired from the National Energy Agency, Malaysia, which is used to identify the catchment boundary. To assess the impact of climate change on inflow and PMP, rainfall projections in the study area for 2010-2099 by the Regional Hydro-Climate Model of Peninsular Malaysia (RegHCM-PM) were acquired from the National Hydraulic Research Institute Malaysia (NAHRIM), Malaysia. The RegHCM-PM is the dynamically downscaled projections of the Canadian climate center general circulation model CGCM1.

Methodology
The main objective of the hydrological model developed in this study is to simulate the Probable Maximum Flood (PMF). Figure 3 describes the methodology used in this study to develop a hydrological model. A lumped conceptual model known as Mike Nedbor Afstromnings Model (NAM), developed by the Technical University of Denmark, was used for the hydrological modeling of the Temengor catchment. Hydrological model parameters cannot always be directly measured, and therefore, the conceptual models are often lumped on a catchment scale, and the catchment is considered a single unit (Bakhtiari 2018;Li et al. 2020;Smith 1965). A lumped conceptual model was used in this study because it is simple but has a physical basis. The NAM model consists of four interrelated depots to mimic catchment storages: snow, surface, soil, and groundwater storage.
The snow component was not considered as it does not occur in the catchment.
The daily rainfall, evapotranspiration, and inflow data for the period 2007 − 2014 were collected, among which data for 2007-2011 was used for model calibration, and the data for the rest three years (2012-2014) for model testing. Areal rainfall over the catchment was estimated using the Thiessen polygon method from the rain gauge estimations at 8 locations. For this purpose, the mean area weights or the proportion of rainfall that a station contributes to the catchment were determined. The rainfall intensity duration frequency (IDF) for different rainfall return periods was developed using rainfall data for the period 2001-2015. The IDF was used to estimate PMP. Projected rainfall for future periods was also used for the projection of PMP for two future horizons, early (2031 − 2045) and late (2060 − 2075). The PMP of historical and future periods was used in the hydrological model for the generation of PMF to assess the changes in PMF in the Tenmengor catchment due to climate change.

Model development
The Mike NAM model has the following basic input requirements.   The NAM model was calibrated with time-series data of catchment runoff to rainfall to determine the optimal values model parameters. For the modeling of runoff of a day, rainfall and evapotranspiration for the day and of the previous day, and the runoff of the previous day is used as model inputs. The model generates runoff very similar to an observed runoff if a proper calibration is carried out.

Model calibration and validation
In this study, data for 5 years (2007-2011) is used for model calibration. A combination of automated and manual calibration was conducted calibration. The auto-calibration of the model is accomplished by optimizing four objective functions: • The negligible error between the average observed and simulated catchment runoff. • There was a good agreement in the observed and simulated hydrograph (small root mean square error (RMSE)). • Good agreement between observed and simulated peak flow in timing, rate, and volume. • A good relationship between the observed and simulated low flows.
After the auto-calibration, manual calibration of nine model parameters was adopted to obtain an accurate agreement between the observed and simulated inflow.
The calibrated model is then validated with observed data (2012-2014).

Model assessment
Both numerical and graphical approaches were utilized to assess the model's accuracy. The graphical approach was used for interpretation, visualization, and qualitative evaluation of model outputs, while numerical evaluation was conducted objectively to assess the model performance. Besides, the statistical indices were used to assess the error and association between observed and modeled runoff. Many researchers gathered a list of performance indicators that are most commonly used in hydrologic modeling (Ehteram et   where Q obsi and Q simi represent the observed and simulated discharge respectively at the time i and n is the number of data used.

Development of rainfall intensity duration frequency curves
IDF is a relationship between duration, intensity, and the rainfall's return period, which is often needed to plan and design different water resource projects. Several equations have been developed for the estimation of IDF. Frequency analysis techniques are often utilized to estimate the rainfall intensity for various return periods by using rainfall data. This study fits the rainfall frequency distribution with type I extreme value (Gumbel) distributions. The probability distribution function (PDF) is utilized to compute the observed rainfall intensity and duration for various return periods to generate the observed IDF curves. The PDF is then used to estimate maximum rainfall intensity for different durations for the return periods of 5, 10, 20, 50, 100, 500, and 1000 years.

Estimation of probable maximum precipitation
PMP in this study is developed using Harshfield Method. The probable maximum precipitation (PMP) is defined as the highest depth of rainfall for a given duration that is

Mike NAM model calibration
To model the runoff of the Temengor reservoir catchment, the Mike NAM model is first calibrated using observed daily data for the period 2007-2011. Nine parameters of the Mike NAM model are calibrated for accurate modeling of runoff. The list of the optimized parameters and their range is given in Table 2. The parameters values were optimized using input (rainfall and evapotranspiration) and the catchment's output (observed inflow) data. The optimum values for each parameter were selected for the proposed model when the gap between the simulated and observed hydrograph was reduced. The simulated and observed inflows for the Temenggor catchment are shown in Fig. 4a. It can be observed that the simulated model performed well during the calibration period.  Figure 4b shows the simulated and observed peak flow for two high rainfall events. The figure reveals that the proposed model can simulate the peak inflow accurately during extreme rainfall events. However, the proposed model could not accurately simulate the inflow during the low flow period as the peak flow as shown in Fig. 4c. One of the challenges of hydrological model calibration is that it is very difficult to accurately represent high and low inflow. Despite that, the emphasis in this study is given for accurate simulation of high inflow as flood forecasting is the study's main objective. The results revealed that the model could reflect the hydrological response of the Temenggor catchment to high rainfall for generating extreme flow.
Scatter plots (normal and log scales) were used to demonstrate the accuracy of the calibrated model in predicting inflow hydrograph for Temenggor catchment (Fig. 5). The scatter plot in normal scale (Fig. 5a) shows that all the points are concentrated along the diagonal line of the plot, which indicates the ability of the model to simulate all the values of observed inflow. The scatter plot in log-scale is prepared to present how the model can replicate the high and low flow. Figure 5b shows that all the high values are very close to the Fig. 5 Scatter plot of daily observed and simulated inflow during the calibration period. a Normal scale; b logarithmic scale, c relative residual plot of daily inflow during model calibration diagonal line of the plot, which indicates the ability of the model for accurate simulation of observed high flows. The low flow values were scattered, which means less capacity of the model to simulate the low flow accurately. Additionally, the relative residual in observed and simulated inflow [(Qo -Qs)/Qo] against the observed inflow is shown in Fig. 5c. The zero values in the plot reveal a good match between the simulated and the observed inflow. The figure shows zero relative residuals for high flow and very close to zero for medium flow. The relative residuals for the low flow values were high. This proves the superiority of the proposed model to simulate the high flow accurately.
To better present model capability, the monthly time series of observed and simulated inflow were prepared and presented in Fig. 6. There was a good match between the monthly observed and simulated inflow. Finally, the model performance was evaluated, and the values of the statistical indices that include RMSE, MAE, MRE, R 2 , NSE, IA, PCC, EI, RSR are found to be 34.94 (m 3 /s), 29.02 (m 3 /s), 0.1 (m 3 /s), 0.87, 0.74, 0.93, 0.87, 0.88, and 0.51 respectively. The errors in the model simulation were low, and the association of observed and simulated inflow was high in terms of all statistics. The NSE value was 0.74, and the RSE was 0.51, which indicates the model's good performance.

Mike NAM model validation
The calibration of the model is validated with inflow data for the period 2012-2015 to show the capability of the model in forecasting inflow for unknown rainfall. Both numerical and graphical approaches are used to evaluate the model performance during the validation period. Graphs are prepared for the validation period similar to those prepared for the calibration period. Figure 7a shows daily observed and simulated inflow to Tenmengor reservoir during the validation period. The ability of the model to simulate peak flow is presented in Fig. 7b that shows the observed and simulated inflow hydrographs from December 2012 to April 2013. The figures show that the model can accurately simulate the daily inflow. The peak flow during high rainfall events can be reliability simulated by the model.
Scatter plots (Fig. 8a) during model validation also show good accuracy of the simulated inflow in replicating observed inflow. The log-scale scatter plot (Fig. 8b) shows that almost all the values are very close to the diagonal line of the plot. The relative residual plot (Fig. 8c) shows almost zero relative residuals for all the flows. The monthly time series of observed and simulated inflow (Fig. 9) shows a good match for nearly the whole calibration period.

Rainfall intensity duration frequency curves
The IDF curves are generated in this study using the areal rainfall data of the Tenmengor catchment. Gumbel PDF is then used to estimate the maximum rainfall intensity for different durations for the return periods of 5, 10, 20, 50, 100, 500, and 1000 years. Using the IDF curves, the estimated rainfall depth was 89.5 mm, 106.3 mm, 143.3 mm, 159.0 mm, 195.1 mm, and 210.7 mm for 5, 10, 50, 100, 500, and 1000 years return period, respectively. The results are found consistent with previous findings. Noor et al. (2018) estimated the IDF curves for Peninsular Malaysia with uncertainty and found similar results.

PMP hyetograph
PMP hyetograph is prepared using data of 1-day rainfall as the ordinate and the duration of the rainfall as the abscissa to examine the peak rainfall time and the temporal pattern of the rainfall. Figure 10 reveals that the highest 1-h rainfall is observed for 11 h, 12 h, and 13 h in a day where the rainfall exceeds 31.014 mm in a day, for which the PMP value is 402.445 mm. These rainfall values were used as input in the calibrated and validated stages of the Mike NAM rainfallrunoff model. The obtained values are multiplied with the fraction of 1-day rainfall to obtain PMF.

Climate change impact on PMF
Rainfall projections of the study area for 2010-2099 by RegHCM-PM are used to assess the impact of climate change on inflow and PMF. The PMF is estimated for two future periods, 2031 − 2045 and 2061 − 2075, for representative concentration pathway (RCP) 8.5. RCP8.5 is used in this study to show the maximum possible impact on PMF in the study catchment due to climate change. Extreme rainfall data during those periods are used in the Mike NAM model to generate inflow. The generated data is then used to estimate PMF for future periods. Finally, the projected PMF data is compared with that obtained for the observed period (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015) to assess the impact of climate change on floods in the Tenmengor catchment. Figure 11a shows the estimated PMF hydrograph for a 1-day storm duration for 2001-2015, while Fig. 11 b and c show the PMF hydrograph for 2031-2045 and 2061-2075, respectively. The summary of the results obtained using PMF hydrograph for 1-day storm duration for Temengor catchment is presented in Table 3.
Climate change caused a gradual increase in extreme rainfall and floods globally (Pour et al. 2020a). Historical changes in rainfall showed an increase in rainfall extremes in Peninsular Malaysia (Khan et al. 2019;Sa'adi et al. 2019;Fig. 8 Scatter plot of daily observed and simulated inflow during the validation period, a normal scale; b logarithmic scale, c relative residual plot of daily inflow during model validation Pour et al. 2020b). A recent study by Khan et al. (2019) showed a significant increase in 1-day and 5-day cumulative rainfall over Peninsular Malaysia. Pour et al. (2020b) showed that the sea surface temperature (SST) of the southeast China Sea is significantly related to rainfall extremes of the region. The global warming-induced rise in SSE may be the cause of increased rainfall extremes in Peninsular Malaysia. Noor et al. (2019aNoor et al. ( , 2019b evaluated the global climate model and used their simulation to project rainfall over peninsular Malaysia. Their findings were very similar to those observed in the present study. They showed an increase in different extremes of rainfall, including intensity. A recent study by Salman et al. (2020) also showed an increase in rainfall extremes.
Increased rainfall extremes have increased flood risk in peninsular Malaysia (Ziarh et al. 2021). The present study showed a large increase in 1-day maximum rainfall and, therefore, PMF in the study catchment. The PMF provides a theoretical estimate of possible flood extremes. Increased PMF due to climate change indicates more severe floods in the study area in the future. Necessary adaptation measures should be considered to protect the Perak River hydroelectric scheme in the basin to the possible increase in rainfall extremes and floods due to climate change.

Conclusion
This study was conducted to assess the impacts of climate change on PMF in the Tenmengor catchment located in peninsular Malaysia. The study provided an understanding of PMF changes due to changes in rainfall in a tropical region where extreme rainfall is more sensitive to global warming-induced temperature rise. A large increase in PMF (48.9% and 122.6% during 2031 − 2045 and 2060 − 2075 respectively) has been projected for the Tenmengor catchment. The increase is mainly due to the large increase in PMP in the catchment. The study corresponds to the previous findings that extreme rainfall would increase more in the tropical region than in the other parts of the globe, which would cause more devastating floods. Policymakers can use the study's findings for adaptation planning and decision-making on climate change. The information derived in this study can help design critical hydraulic infrastructure to mitigate floods. The rainfall projections used in this study are based on the dynamical downscaling of only one GCM through a regional climate model. A large uncertainty is associated with GCM simulation, and therefore, rainfall projections of other GCMs can be used to assess changes in PMF and the associated uncertainty. The study can also be conducted to assess the changes in PMF for different emission scenarios for facilitates better decision-making on designing factors of hydraulic structures.