Spillway Capacity Estimation Using Flood Peak Analysis and Probable Maximum Flood Method

: This study aims to assess a spillway’s capacity to manage the highest possible fluctuations in water levels, the probable maximum flood (PMF). The PMF values have experienced alterations throughout the last six decades since the initial design and construction of the Kaeng Krachan Dam, one of Thailand’s major dams. The study also conducted an assessment of the greatest levels of rainfall for different timeframes, known as probable maximum precipitation (PMP). This was achieved by simulating the movement of rainstorms into the reservoir area near the dam. After-wards, a thorough examination was carried out on several time periods related to anticipated flood volumes, PMF, and the spillway’s capability. The research entailed a comprehensive analysis of rainfall occurrences spanning 65 years, encompassing a total of 190 storm events, to present the top 10 highest recorded levels of rainfall in the southern and western regions of Thailand. This information is of utmost significance in assessing the potential maximum rainfall in the study area. The results reveal that the highest PMP observed over a three-day period was 429.20–726.40 mm, which is slightly different from the results obtained using storm transposition method (513.90–869.76 mm). Results of PMF and base flow were 4677.00 and 86.80 cms, respectively. The results of the examination of the estimated maximum flood volumes and their comparison with previous studies show that the maximum flow rates per unit area are within reasonable and consistent boundaries. The current spillway has the capability to manage flood flows with a frequency of up to 10,000 years. Nevertheless, while examining the potential PMF, it has been concluded that the existing spillway’s capacity is insufficient to adequately handle the highest water level in the reservoir, therefore preventing it from exceeding the designated maximum water level.


Introduction
The probable maximum precipitation (PMP) and the probable maximum flood (PMF) are crucial pieces of information in the water resource engineering area.PMP refers to the highest amount of precipitation that can occur at a specific place and during a time frame.It can be calculated using two main methods.Firstly, there is the physical technique, where meteorological data is applied.Here, for example, dew point temperature and wind speed might be used for estimation.The second type involves statistical methods, such as Hershfield's approach.In general, the first is more common because it takes into account a large amount of meteorological data [1].
PMF is defined as the highest flood level that is anticipated to occur at a particular location and time.Generally, PMF is employed to estimate the flood characteristics of hydraulic structures and provide flood protection information for vulnerable areas.It also represents an upper limit for the range of conditions that dam operators need to be aware of.Typically, PMP and PMF are approximated based on the most extreme combination of meteorological and hydrological factors [2].
It is widely acknowledged that the climate situation has been altered as a result of the current climate change crisis.Climate change impacts multiple domains, including hydrological and water resource systems.The fluctuations in rainfall patterns and amounts over the past few decades have led to an alteration of the occurrence of extreme incidents.Ref. [3] indicates that PMF estimates are primarily influenced by meteorological factors, climatic change conditions, antecedent soil moisture, changes in land use and land cover, and reservoir storage and operation.In addition, climate factors, such as the presence of atmospheric moisture have led to seasonal and persisting dewpoint temperature increases.These have resulted in an increment in the moisture maximization of storms and higher PMP estimates, with a change of around 13-38% under climate change situations in Australia [4].Similar to the research conducted in [5], the study observed an approximate increase of 8-20% in PMP, while PMF showed an increase of roughly 20% in some regions of the Canadian basin, though some locations showed a decrease.The study in [6] focused on the effects of climate change and land use changes in a worst-case scenario in northern Thailand.Their findings reveal that a 5% rise in PMP results in a 7.5% increase in PMF.Moreover, a decrease in wooded regions ranging from 10% to 30% led to a corresponding rise in PMF of 3.1% to 9.2%.
Kaeng Krachan Dam is the greatest dam in the Phetchaburi-Prachuap Khiri Khan River Basin, one of Thailand's 22 major basins.This dam was constructed and completed in 1966 and has been successfully operated for more than 50 years, similar to most of the large dams in Thailand that were designed and constructed during the 1960-1980 period and are still in operation now.The dam, which has a maximum water storage capacity of 900 million cubic meters, plays a crucial role in addressing flood-related challenges in the province of Phetchaburi.After a long period of operation, the physical characteristics of the catchment area of the dam may have changed due to various causes, for example, climate change conditions, population increment, deforestation, and land use change.With the climate change condition, this basin is expected to experience rainfall increments [7], especially over the long term (2051-2099).Deforestation was also found to be a factor in the work of [8].Their results reveal that forest was reduced by around 401 km 2 in Kaeng Krachan National Park, the catchment area of Kaeng Krachan Dam.In addition, the study of the PMP and PMF for designing the dam in the past may have been constrained due to data limitations.Hence, there is a need to analyze the alteration in order to mitigate the potential risks that could result from future catastrophic events.
This study aims to investigate PMP and PMF, as well as assess the spillway's ability of the Kaeng Krachan Dam to manage floods and maintain the dam's stability.Rainfall return period and storm transposition method were employed in this study.Rainfall data and storm occurrences were collected and analyzed over 65 years.The results of this study will support the relevant agencies, such as the Royal Irrigation Department in Thailand, for the operation and preparation of dam safety.

Study Area
Kaeng Krachan Dam is located in Phetchaburi province, in the western part of Thailand (Figure 1) with a catchment area of 2210 km 2 .The dam storage and the maximum storage are 710 mcm and 900 mcm, respectively, and comprises an ungated spillway with a weir of 110 m that is able to release water with a maximum amount of 1380 m 3 /s.The water is delivered to the Phetchaburi Operation and Maintenance Project for expanding an irrigation area from 342 km 2 to 538 km 2 during the rainy season and supporting agricultural areas of around 278 km 2 during the dry season.In addition, the water from this dam is mainly used for consumption and tourism in Hua-Hin district, which is the most attractive area in the basin.

The Analysis of Maximum Rainfall at Different Return Periods
The procedure entailed the selection of rain gauge stations to function as index stations.A total of four stations were chosen within the rain catchment area of the Kaeng Krachan Dam and its surrounding regions.Following that, information regarding the highest levels of rainfall recorded over periods of 1, 2, and 3 days each year was gathered from the 4 stations mentioned.These data encompass the time frame between 1965 and 2015.The data that were gathered were subsequently examined to determine the highest levels of rainfall that occurred over a period of 1 to 3 days at each station on an annual basis.The investigation utilized the Gumbel distribution approach, which is a theoretical framework commonly used for frequency distribution analysis in Thailand, and as examined by [9].The goal was to calculate the greatest amount of rainfall that may occur during a period of 1 to 3 days for different recurrence intervals.In addition, a spatial study was performed to examine the distribution of rainfall in the rain catchment area north of the Kaeng Krachan Dam.The Thiessen weighting factor method was utilized to determine the maximum rainfall values for each year and repetition interval.

The Analysis of Probable Maximum Precipitation (PMP)
The storm transposition method recommended by the World Meteorological Organization [10] was considered for use in this study.The study entailed an examination of historical and current rainfall data in Thailand.In this study, the rainfall data obtained from the Thai Meteorological Department [11] were examined for a period of 65 years, ranging from 1951 to 2015, which included a total of 190 storms.The study area, which was the watershed of the Kaeng Krachan Dam, specifically focused on large-scale storms that occurred in the same geographical region.The selection process was conducted by considering the highest recorded rainfall levels throughout a 3-day timeframe.These data were then compared with the actual recorded rainfall data to determine the rainfall quantities for each storm, which varied from 1 to 3 days.The information regarding the storms and the weather stations that contributed to the highest amount of rainfall can be found in Table 1.The 10 highest rainstorms of the 14 that influenced the west and south of Thailand were then carefully selected.The storm tracking map is shown in Figure 2.  Air moisture correction factors were calculated regarding moisture value, geographical characteristics, locations of storm origination, and the study area.The first correction factor (r1) was the adjustment of air moisture at the area of storm occurrence.The ratio of probable maximum air moisture at the storm location with h1 level ((W m1 ) h 1 ) and probable air moisture at the day storm occurring at h1 level ((W S ) h 1 ) was calculated.Here, h1 (msl) is the highest level of the storm location or the level of obstruction between the source of air moisture and the storm location.
The correction value of air moisture at the transposition area was then calculated by consideration of the 12 h maximum dewpoint at 1000 mbar at the location of the storm occurrence and the transposition area.These results were then adjusted to probable air moistures and the second correction factor (r2) was computed using the ratio of the probable maximum air moisture between the transposition location and the area in which the storm occurred.
The adjustment of elevation and barrier was then investigated.This method was applied when both elevation and barriers, such as a mountain range, were shown between the location of storm generation and the rainy area.The storm transposition with a low difference level, of less than 300 m, was not required for adjustment.However, the one showing a large difference in level, higher than 700 m, was recommended to be adjusted by the ratio of the 12 h dewpoint at 1000 mbar for the transposed location.The value was then computed for air moisture.Finally, the ratio (r3) between the probable maximum air moisture at the transposed area at the h1 and h2 levels was calculated.
The term (W m2 ) h 1 reflects the maximum potential atmospheric water content at the place shifted to level h1, measured in millimeters.The term (W m2 ) h 2 reflects the maximum potential atmospheric water content at the place shifted to level h2, measured in millimeters.h 2 represents the highest value of the level at the specific point that has been displaced, or the level of the barrier between the source of moisture and the displaced position.This measurement is expressed in meters above the mean sea level.
The analysis entails an examination of the components that contribute to the combined rainfall between the method with the maximum precipitation and the method of redistributing the rainfall.This involves taking into account the moisture correction value for the highest amount of rainfall at the initial location of the storm (r1) in Equation ( 1) along with the moisture correction at the new place (r2) in Equation ( 2) and the correction caused by the sea level and barrier (r3) in Equation (3).The calculation of the total correction value (rm) involves taking into account factors such as moisture, the elevation relative to the mean sea level, and the presence of barriers, as described by the following equations: The adjustment index accounts for the topography, as Thailand predominantly features a flat environment with minimal slope requirements.This investigation specifically examines how geographical changes impact the behavior of storms, utilizing the adjustment percentage of annual or seasonal rainfall, known as HMR46 [12].The average seasonal rainfall and number of rainy days per season in the southern part of Thailand from October to December were calculated using monthly average rainfall data and the number of rainy days from 654 rain gauge stations across Thailand for the years 1951-2009 [13].The investigation utilized GIS software (ArcGIS 10.5) to produce maps that depict the adjustment index resulting from the terrain, as depicted in Figure 3.The adjustment index, which was determined by the proximity to the sea, was derived from the idea that precipitation diminishes as one moves further away from the coastline or moisture origins.The upper limit for the amount of rainfall during storms that happened along the coastline was established at 1. Subsequently, the storm was displaced, and the value was modified according to the proximity to the ocean using Schwarz's methodology [14].Figure 4 displays the map illustrating the adjustment index according to the proximity to the sea.The HMR46 adjustment index [12] accounts for the attenuation of tropical cyclones as they approach the centerline and their strengthening while located north of the 15th parallel.The intensity diminishes linearly by 2.5 percent per degree of latitude from the 15th parallel to the 10th parallel.Gray's analysis [15] showed a dramatic decrease in intensity near the 4-5 degree parallel.Figure 5 displays the map that represents the adjustment index according to latitude.
The comprehensive adjustment index can be generated by combining all adjustment indices, such as humidity, sea level, obstacles, topography, distance from the sea, and latitude.The comprehensive adjustment index was obtained by computing the entire adjustment based on both the storm movement position and the storm occurrence position reference points.Tables 2 and 3 contain the specific placements and adjustment indices for rainfall that affect the catchment area of the Kaeng Krachan Dam.The storm shifted towards the Kaeng Krachan Dam, which is situated at an elevation of 94.00 m above mean sea level and showed a maximum dew point of 26.37 °C.

Area Rainfall Reduction Factor Analysis
This study applied the areal rainfall reduction factor (ARF) for the reduction of rainfall amount, which depends on area size.The first ten strongest storms that occurred in the south of Thailand were used for the calculation.The different rainfall loss rate factors related to various return periods suggested by [16] were used.Figure 6 presents areal rainfall reduction factors for the southern part of the country.

Analysis of Probable Maximum Flood (PMF)
This study utilized unit hydrograph techniques, as advised by the U.S. Department of the Interior Bureau of Reclamation [17], to convert peak maximum precipitation (PMP) values into probable maximum flood (PMF) values.The examination of a solitary-unit hydrograph was separated into two stages.The initial stage involved establishing the correlation between the parameters of a single-unit hydrograph and the parameters of the watershed and river.In the second stage, the developed relationship equation was utilized to compute the single-unit hydrograph for the rainwater-receiving area of the Kaeng Krachan Dam.
The equation that describes the connection between the parameters of a single-unit hydrograph and the parameters of a watershed-river was derived from data collected from multiple water measurement stations in the southern region.This equation was used for the study area, based on the findings of a study conducted by the Hydro-Informatics Institute [18].The equation is represented as follows: tp = 1.2636 (LLc/(S 1/2 )) 0.2956 (6) qp/A = 0.5379 (tp) 1.2642 (7) where tp is the duration of maximum discharge (hour), qp is the maximum discharge (m 3 /s), L is the length of the main river (km), Lc the length of the main river from the outlet to the center of the river (km), S is the slope length of the river (%), and A is the catchment area (km 2 ).Based on the given relationships and the watershed-river characteristics of the northern watershed of the dam, the parameters for a hydrograph unit for the rain-receiving area located north of the Kaeng Krachan Dam were computed.The parameters of the watershed-river system, A, L, and Lc, were 2210 km 2 , 119.09 km, and 50.17 km, respectively.The values of the average slope of the river (Savg) and maximum slope of the river (Smax) were 0.0019 and 0.00579, respectively.In addition, a single-unit hydrograph was utilized with a time interval (tr) of 24 h, tp and qp of 41 h, and 108.7 m 3 /s.Equation (8) defines the relationship between the base flow (QB) and maximum flow of the hydrograph (QP) as presented in Equation ( 8) and as studied by [19].QB = 0.2825 QP 0.6793 (8)

Estimation of Spillway Capacity
The spillway capacity of Kaeng Krachan Dam can be estimated using the results of the change in maximum floods discharging to the reservoir and flowing through the spillway together with the highest water level in the reservoir.Surcharge and freeboard levels of the dam were also considered so as to be aware of the safety of Kaeng Krachan Dam.
The Kaeng Krachan Dam has an overflow weir spillway with a length of 110.0 m, and the level of weir and maximum flood are +99.00m (msl) and +102.65 m (msl), respectively.The maximum discharge is 1380.00m 3 /s.Flood routing analysis developed by [20] was used in this study (Equations ( 9) and ( 10)), where S is storage (m 3 ), I is water flow into the reservoir (m 3 /s), O is water discharge out of the reservoir (m 3 /s) and t and i refer to time (s) and time-step used for each study, respectively.

Maximum Rainfall at Different Return Periods
The Gumbel distribution method was selected to be applied for return period analysis using rainfall amounts measured by four rain gauges.The Thiessen weighting factor was also used for the areal average rainfall calculation of Kaeng Krachan Dam.The highest daily rainfalls for three days of each return period are presented in Table 4.As expected, the 10,000-year return period produced the highest rainfall with 378.52 mm for three days, whereas the 2-year return period gave a rainfall amount of 65.11 mm for only one day.

Probable Maximum Precipitation and Maximum Flood Analysis
Fourteen rainstorm events were considered in order to estimate PMP in the Kaeng Krachan catchment.Table 5 indicates the highest cumulative rainfall period for three days using observed data and the results of the storm transposition method.The highest PMP occurred from 31 October 31 to 4 November 1969 for a tropical depression (storm code: 076) with a rainfall amount of between 429.20 and 726.40 mm for three days.Slight differences of maximum rainfalls between observed/calculated data could be noticeable, with 429.20/513.90, 603.10/722.12,and 726.40/869.76mm for the first, second and third days, respectively.In addition, the observation of maximum floods calculated by storm events at different return periods and probable maximum floods are presented in Table 6 and Figures 7 and 8. Probable maximum flood and base flow were 4677.00 and 86.80 cms, respectively, whereas flood volume was 1057.60 mcm.

Comparing the Results of the Historical PMF Analysis
The comparison results of the analysis of the PMF with the study completed in 1965 are conveniently displayed in Table 7.The PMF obtained from this investigation (4677 cms) was somewhat lower than the previous study's result of 4720 cms, reflecting a difference of only 0.91%.However, while examining the amount of the highest flood, the results show that the calculated volume in this study was 1057.6 mcm.This was more than the volume estimated in the previous study, by 265.2 mcm, or a percentage difference of 398.The significant disparities in results may have arisen from the different methods employed to calculate flood hydrographs from PMP and the data utilized for the investigation.This study was able to access a longer period of the data used for the study compared with the previous one.Comparing the assessment of the PMF for the Kaeng Krachan Dam to the previous study, it was found that the PMF value obtained in this study closely matches the PMF value determined in the historical study.Furthermore, by dividing the PMF value derived from this study by the area that received rainfall, the unit peak discharge was then computed.This may then be graphed to illustrate the correlation between unit peak discharge and rainfall receiving area.The graph was constructed using probability mass function data obtained from 43 dam projects in Thailand, as documented by the Food and Agriculture Organization (FAO) [21].Figure 9 unequivocally illustrates that the PMF value obtained from this research is within a rational range and aligns with findings from prior investigations.

Assessment of the Spillway's Capacity
The analysis of the movement of the maximum diversity graph during annual occurrences and the PMF graph through the spillway is shown in Table 8, based on the study results.Figure 10 illustrates a comparison between the graphs depicting the highest levels of diversity in the inflow and outflow of water through the spillway of the dam.It was observed that, within a recurrence period of 2 to 10,000 years, the highest range of water levels with the most diversity was between +99.70 and +102.10 m (msl).The current level exceeded the spillway crest level, with a range of 0.70 to 3.10 m.However, it still maintained a safe distance from the highest water level to the dam crest (dry freeboard), which was between 3.90 and 6.30 m.The maximum diversity water level was not above the predetermined maximum water level of +102.65 m (msl).The analysis of the PMF water quantity moving through the spillway revealed that the maximum diversity water level was +104.70 m (msl).The current water level surpassed the intended maximum level by 2.05 m and exceeded the spillway crest level by 5.70 m.The distance between the maximum diversity water level and the dam crest, also known as the dry freeboard, was 1.30 m.The findings are presented in Table 8.
The comparison between the maximum diversity water level (+104.70m, msl) and the crest level of low embankment dam No.2 (+102.70 m, msl) indicated that the former was at a greater elevation.Hence, it was imperative to conduct a simultaneous assessment of the greatest possible floodwater volume, known as the potential maximum flood, that might flow over the spillway and traverse low embankment dam No. 2. The embankment dam No. 2 is characterized by its dimensions: a length of 255.00 m, a height of 22.00 m, and a crest level of +102.70 m (msl).The analysis of the maximum possible flood water volume flowing through the spillway and concurrently via the low embankment dam No. 2 is outlined below.
The analytical results for the highest possible flood volume passing via the spillway and low-level outflow of dam No. 2 indicate that the maximum water level is +104.20 m (msl), above the designed maximum water level of 1.55 m.This finding suggests that the dam holds a significant capacity to handle large volumes of water, providing reassurance in its ability to withstand extreme flooding events.Furthermore, the water level exceeded the spillway crest elevation by a significant 5.20 m.The analytical results in Table 9 indicate that there was a leftover distance of 1.80 m from the maximum water level to the dam crest elevation (dry freeboard).

Conclusions and Discussion
The objective of this study was to investigate the capacity of spillways using various approaches, including the probable maximum precipitation, the probable maximum flood approaches, and the storm transposition method.The three-day maximum rainfall for the largest return period (10,000 years) ranged from 209.81 to 378.52 mm.The differences between the results of the maximum PMP of observation and the storm transposition technique for a span of three days were minimal.The PMF and base flow were 4677.00 and 86.80 cms, while the flood volume was 1057.60 mcm.In addition, the comparison of the PMF between this study and the previous one was slightly different.The examination of the PMF for the amount of water flowing through the spillway indicated that the highest water level was +104.70 m (msl) while the level of weir and peak flood at Kaeng Krachan reached +99.00 m (msl) and +102.65 m (msl), respectively.
When it is essential to control the maximum water level of the Kaeng Krachan Dam reservoir to prevent it from exceeding the targeted level of +102.65 m (msl) and for the safety of the dam and adjacent areas, two potential approaches can be considered.An effective non-structural measure entails implementing techniques such as releasing water or reducing water levels in reservoirs to accommodate the maximum probable flood volume.These techniques can aid in reducing the impact of floods and ensuring the safety of the surrounding areas.To achieve an elevation of +82.00 m (msl), it is recommended to lower the water level in the reservoir by 17 m from the typical storage level of +99.00 m (msl).This modification would result in a peak water level of +102.60 m (msl), indicating a rise of 3.60 m compared with the height of the spillway crest.The remaining vertical distance between the maximum water level and the elevation of the dam crest (referred to as dry freeboard) is 3.40 m, ensuring an ample safety margin.
An option for a structural modification is to extend the spillway crest from its existing length of 110 m to 280 m, resulting in an additional 180 m of length.This modification would result in a peak water level of +102.60 m (msl), indicating a rise of 3.60 m in relation to the elevation of the spillway crest.The current distance between the maximum water level and the dam crest elevation (dry freeboard) is 3.40 m, providing a significant safety buffer.The analytical findings have been gathered and are currently accessible for examination in Table 9.In addition, in order to enhance the dam's preparedness for potential future water levels, it is imperative to conduct a thorough examination of the dam's safety through structural modifications based on the findings of this study.The responsibility

Figure 2 .
Figure 2. Paths of the 14 storms that led to the top 10 highest rainfall events, influencing the regions of southern and western of Thailand.

Figure 3 .
Figure 3. Correction factor index derived from the geographical conditions.

Figure 4 .
Figure 4. Correction factor index deriving from the distance from the sea.

Figure 5 .
Figure 5. Correction factor index deriving from latitude.

Figure 6 .
Figure 6.Area reduction factor (ARF) for rainfall reduction based on area size for the lower part of Thailand.

Figure 7 .
Figure 7. Maximum flood for different return periods.

Figure 9 .
Figure 9.The relationship between peak flow values per unit area and the rainfall catchment area [21].

Figure 10 .
Figure 10.Maximum flood peak with various recurrence period and PMF.

Table 2 .
The positions as the rainstorm moved towards the Kaeng Krachan Dam.

Table 3 .
Cumulative adjustment index reflecting the rainstorm approaching Kaeng Krachan Dam.

Table 4 .
Results of the analysis of annual maximum rainfall in the rainwater-receiving area north of the Kaeng Krachan Dam.

Table 5 .
The estimated maximum amount of rainfall that could occur after relocating the precipitation to the Kaeng Krachan Dam.

Table 6 .
The calculation of the maximum flood with different return periods for the Kaeng Krachan Dam.

Table 7 .
Comparison with the previous study of the Kaeng Krachan Dam.

Table 8 .
Analysis results of the movement of the maximum flood through spillway.

Table 9 .
Results of the analysis of the movement of the maximum flood through the spillway and through the low-level outlet structure No. 2.
Note: * as extended length of spillway.