Probable Maximum Precipitation Estimates Research Articles

A Physically Constrained Model-Based Moisture Amplification Approach for Probable Maximum Precipitation (PMP) Estimation

Abstract The flood that would result from the greatest depth of precipitation “meteorologically possible” or probable maximum precipitation (PMP) is used in the design of dam spillways and other high-risk structures. Historically, PMP has been estimated by scaling precipitation totals obtained from severe historical storms, assuming more moisture could have been available. Over the last decade, numerical weather prediction models have been used to instead predict precipitation resulting from the addition of moisture in the simulations [called relative humidity maximization (RHM)]. Despite the major improvement they represent, two important barriers limit the applicability of model-based methods: first, the existence of different moisture amplification approaches that produce different estimates, and second, the need for a regional implementation of those techniques that were developed for individual basins. Taking Oregon’s mountainous coastal watersheds affected by atmospheric river storms as a case study, we develop a moisture amplification approach, which we call relative humidity perturbation (RHP) ratio that is physically constrained by historical maximum moisture. We find that both the magnitude and location of moisture increase matter and that RHP ratio produces lower amplified precipitation totals but storms that are more consistent with observed events than other methods such as RHM. We additionally find that it is possible to position a storm near-optimally over several basins in a homogeneous area, enabling the production of regional PMP estimates. The understanding we develop of the control moisture exerts on PMP-magnitude precipitation totals allows us to develop a more physically based methodology for the development of reliable storm amplification guidance.

Analyzing uncertainty in probable maximum precipitation estimation with large ensemble climate simulation data

AbstractThis study aimed to evaluate probable maximum precipitation (PMP) estimated using surface dew points (SDP) or actual precipitable water obtained from upper‐air data (UAD) in the moisture‐maximization method with the help of sufficient extreme precipitation events using large‐scale climate ensemble simulation data (d4PDF). The deviations between the PMP variables estimated by the SDP and UAD approaches were analyzed for southern and northern areas of Japan to consider the regional characteristics of the deviations. We found that the deviations were high in northern areas where the SDPs are relatively low during precipitation events. The PMPs estimated using each approach were also compared to the extreme‐scale reference precipitation proposed in this study. The SDP approach overestimated the PMPs by over 20% compared to the reference precipitation in the northern region. However, the UAD approach showed very low average errors in all southern and northern areas. This tendency of the SDP approach was significantly related to the regional climatic characteristics of the SDP, which indicated that the SDP approach may estimate an uncertain PMP value depending on each regional climatic characteristic compared to the UAD approach. Regional climatic characteristics should be considered when using the SDP approach to estimate the PMP.

Re-inventing Bethlahmy method for estimating probable maximum precipitation

The design and risk analysis of large-scale hydraulic structures (e.g., dams) and sensitive installations (e.g., nuclear facilities) downstream of those structures rely on design flood corresponding to probable maximum precipitation (PMP). In areas where there is a sparsity of information on hydrometeorological variables, practitioners use various statistical methods to arrive at a PMP estimate, assuming it to be the possible upper bound for precipitation. However, the assumption is violated in different parts of the world. Hence, there is a need to improve the existing statistical methods and develop their potential alternatives. Against this backdrop, this paper proposes a new variant of a non-parametric method (Bethlahmy) to facilitate the estimation of PMP at locations with sparse records of extreme precipitation. It involves mapping of datapoints in annual maximum series and their ranks to a non-dimensional space (NDS) and using the information on sample size and observed maximum precipitation in the NDS to arrive at a surrogate variable representing PMP, which is eventually mapped back to PMP in the original space. The effectiveness of the proposed Bethlahmy variant over various existing statistical techniques is illustrated through Monte Carlo Simulation experiments and a case study on 37,872 stations from a global precipitation database. The existing techniques include the original Bethlahmy and Hershfield methods, conventional probabilistic approach, and relevant variant(s). Insight is provided into the relative performance of these methods, as there is a dearth of such attempts in the literature. Results indicate that the proposed Bethlahmy variant exhibits better performance than other methods/variants across samples varying in size and extreme precipitation characteristics, making it a promising statistical alternative for PMP estimation.

Validation of Hershfield probable maximum precipitation estimation using homogeneous region in Malaysia

Probable maximum precipitation (PMP) is used to design major hydraulic structures, such as dams and spillways, flood protection works, and nuclear power plants. Long observation data are required for PMP estimates using the Hershfield statistical approach. In Malaysia, the PMP calculated using state boundary is commonly used, but the estimated PMP values are close to historical maximums. Homogeneous regions are regions containing stations with similar rainfall characteristics. Therefore, homogeneous region boundaries could be used for PMP estimations. In this paper, 1-day rainfall data of more than 25 years for 161 stations in Peninsular Malaysia; were analysed to estimate the PMP for 1-day duration based on an appropriate frequency factor by considering homogeneous regions. Using PMP estimates, a generalised graph was prepared to show the spatial distribution of 1-day PMP. The 1-day PMP estimates in Peninsular Malaysia by considering state boundary, varied from 146 to 1364.7 mm and by considering the homogeneous regions, the 1-day PMP estimates varied from 208.5 to 2094 mm. Hence, the PMP considering homogeneous regions is considered more accurate and safe to be used in designs.

Improving Confidence in Model-Based Probable Maximum Precipitation: How Important is Model Uncertainty in Storm Reconstruction and Maximization?

Abstract We analyze uncertainty in model-based estimates of probable maximum precipitation (PMP) as used in dam spillway design. Our focus is on model-based PMP derived from Weather Research and Forecasting (WRF) Model reconstructions of severe historical storms, amplified by the addition of moisture in the boundary conditions [so-called relative humidity maximization (RHM)]. By scaling moisture and predicting the resulting precipitation, the model-based approach arguably is more realistic than currently used techniques [documented in NOAA’s Hydrometeorological Reports (HMRs)], which assume that precipitation scales linearly with moisture. Despite the important improvement this represents, model-based PMP is subject to several sources of uncertainty that have slowed adoption in operational settings. We analyze an ensemble of PMP simulations that reflect recognized sources of uncertainty including the following: 1) initial condition error, 2) choice of physics parameterizations, and 3) upscale propagating model errors. We apply this ensemble approach to the Feather River watershed (Oroville Dam) in California for the storms of February 1986 and January 1997, which produced some of the largest floods on record at that location, after carrying out in-depth evaluations of model reconstructions. Differences in the maximized 72-h precipitation totals across the 56 ensemble members we produced for each storm are modest, ranging from ±7% of ensemble mean. Our results suggest that while model-based PMP estimates should be interpreted as a range of values, model uncertainty appears to be relatively small for the major atmospheric river–driven flood events we investigated.

Estimation of Probable Maximum Precipitation at Talar Basin of Mazandaran Province using Synoptic Method

Estimation of Probable Maximum Precipitation at Talar Basin of Mazandaran Province using Synoptic Method

The Impact of Climate Change on Operational Probable Maximum Precipitation Estimates

AbstractThe safety of high‐risk water infrastructure, such as dams and nuclear power plants, is often assessed by reference to their ability to accommodate floods derived from the Probable Maximum Precipitation (PMP). However, a key shortcoming of traditional PMP estimates is the assumption of a stationary climate, with evidence indicating that key meteorological conditions related to the magnitudes of extreme storms, such as atmospheric moisture, are changing in a warming climate. Due to the pragmatic nature of PMP methods derived for design purposes, inferring potential changes in PMP estimates based solely on trends or projections of atmospheric variables can ignore PMP method complexities and constraints. Here we explore how different traditional PMP methods will respond to a potential increase in atmospheric moisture. We find that increases in persisting dewpoint will lead to increases in PMP estimates, and the nature of this impact depends on whether the moisture maximization step is based on local or transposed regional information. An historical trend analysis reveals annual maximum persisting dewpoint temperatures have increased continuously over Australia over the past 60 years, with further increases predicted over the coming decades for all Shared Socioeconomic Pathways (SSPs). PMP estimates across Australia are predicated to increase by an average value of 13% by 2100 based on the conservative SSP1‐2.6, compared to 33% for SSP5‐8.5. We conclude PMP methods will require regular updating to account for changing persisting dewpoints and likely progressive increases in PMP, and the ensuing flood estimates.

Estimation of probable maximum precipitation 24-h (PMP 24-h) through statistical methods over Iran

Abstract Estimating the probable maximum precipitation (PMP) is necessary to calculate the probable maximum flood (PMF). It is of high importance in checking the adequacy of dam overflow capacity and other development and water transfer plans of a given area. In this research, using the for an annual 24-hour maximum rainfall data set of 45 synoptic stations throughout the country, the PMP values were calculated through the original Hershfield method and then the Hershfield-Desa method. By comparing the obtained results of 24-hour PMP estimation through the two mentioned methods, it is found that the estimation of PMP values in the original/first Hershfield method is well higher than the expected value (2.54 to 4.03). While in the modified method (Desa method), PMP values are significantly reduced and seem more reasonable (1.02 to 1.3). Meanwhile, the calculated variability and skewness coefficients also indicated more variability of PMP values in the southern stations of the country compared to rainy regions, which makes the estimation of PMP in the southern regions of the country considerably unreliable.

Application of the British Columbia MetPortal for Estimation of Probable Maximum Precipitation and Probable Maximum Flood for a Coastal Watershed

Estimation of the Probable Maximum Precipitation (PMP) and Probable Maximum Flood (PMF) are regulatory requirements in many jurisdictions that are used in the design of dams and assessment of existing infrastructure. The recently available British Columbia MetPortal provides regionally consistent PMP and precipitation frequency estimates across the province of British Columbia (BC). This paper proposes an approach to process and apply this data for the estimation of the PMF for watersheds across British Columbia. Guidelines are presented for selection of transposition points applicable to a watershed, and algorithms are developed for processing the geospatial probable maximum storm and precipitation frequency data. The algorithms developed are generic to multiple software and programming environments, and could also be applied in other regions where spatially and temporally intact PMP estimates are available. A detailed description of data sources and development of PMF scenario inputs is provided, as well as details of important sensitivity analyses. The methodology is applied to estimate the PMF for the Cheakamus Basin north of Squamish British Columbia. The application of the MetPortal PMP and precipitation frequency estimates, when used with a consistent PMF development methodology as proposed in this paper, will help improve the consistency of PMF estimates for watersheds across the province, offering a welcome improvement for dam owners and regulators.

Historical trend of probable maximum precipitation in Utah and associated weather types

AbstractThis study assesses the impact global climate change has had on the theoretical upper limit of precipitation for Utah's watersheds by examining historical trends in probable maximum precipitation (PMP), a metric widely used for dam construction and management. Trends in the factors of PMP driven by both frontal and monsoonal storm scenarios were studied using two networks of surface weather stations and modern gridded datasets spanning 1981–2018. It was found that the historical trend in both 3‐hr and 24‐hr PMP estimations exhibited a statistically significant increasing trend, despite that the magnitude of the trend was sensitive to which dataset was examined and the data's spatial resolution. Over the 24‐hr time scale, an interesting deviation in PMP trends was found where frontal storm events demonstrated increasing PMP trends compared to decreasing PMP trends for monsoonal storm events. However, both storm types demonstrated increasing trends over shorter 3‐hr durations, suggesting a universal increase in convective storm intensity. PMP estimates also demonstrated a dependency on the type and resolution of meteorological data used, where higher‐resolution data generally produced greater PMP values and weaker trends. A discussion on the potential causes of these dependencies is provided. This study implies the need to take the historical PMP trend into account for future PMP estimates, especially when coarse‐resolution data are used for conventional PMP studies.

Study on PMP estimation for the flood risk evaluation of hydropower dams in consideration of the future climate change

It is important for hydropower dams to estimate PMP (Probable Maximum Precipitation) appropriately and to prepare the plan of facilities modification and operational changes in advance, because the future flood risk by climate change influence is getting higher. In this paper, we compared three methods of PMP estimation, the conventional method applying DAD (Duration Area and Depth) analysis based on the experienced rain results, the product of d4PDF (database for Policy Decision making for Future climate change) that is the latest climate model ensemble prediction, and the pseudo-global warming experimental results on the typhoon. It was showed that PMP by d4PDF and the pseudo-global warming experimental results were larger than that by DAD analysis and fluctuated smoothly and reasonably over time. It is preferable and reasonable to evaluate the PMP risk applying DAD analysis at the rough examination, and the estimations applying d4PDF or pseudo-global warming scenario is suitable for more detailed examination.

Estimation of probable maximum precipitation of a high-mountain basin in a changing climate

Abstract To estimate the probable maximum precipitation (PMP) in a changing climate, this study proposes a new PMP estimation framework based on weather research forecasting (WRF) initialed with temperature (predicted by post-processing) for changing climate conditions. First, in order to determine temperature disturbance influencing PMP under climate change, a random forest (RF) model considering error correction is introduced to predict the temperature in the future. Results show that the revised RF model could improve accuracy in temperature prediction. Furthermore, numerical experiments of disturbance amplification of three factors (humidity, wind speed, and temperature) using the WRF model are conducted. This new scheme could consider the effect of three elements (horizontal range, vertical layer, and ratio) of influencing factors’ maximization on PMP. Results indicate that for the most unfavorable precipitation scenario of each factor magnification, the combination of three elements is different. Then, the joint amplification numerical experiments of three factors proved the existence of their interactions when multi-factors changed simultaneously. Finally, this method was tested in a high-mountain basin, the Upper Nujiang River Basin. Results showed that the increase of wind speed plays a leading role in rainfall enhancement, and the rising of relative humidity and temperature has a certain disturbance effect on rainfall.

Estimation of Long-duration Maximum Precipitation during a winter season for large basins dominated by Atmospheric Rivers using a Numerical Weather Model

The Probable Maximum Precipitation (PMP) estimation for long durations during winter and spring seasons is important to develop the Probable Maximum Flood for snowmelt-driven regions since extreme floods are often characterized by snow-accumulation and snowmelt processes rather than by a single rainstorm event. Although several studies have estimated the PMP for a single storm duration, little attention has been given to the PMP estimation for long durations on the order of several months. This study proposes a new framework using a numerical weather model (NWM) to estimate the long-duration Maximum Precipitation (MP) during the winter season, which is the first part of a two-part effort to develop the PMP during the winter and spring seasons. As a demonstrative case, we estimate the MP for the 6-month winter period (October to March) for the drainage areas of Bonneville Dam (621,600 km2) and Libby Dam (23,270 km2) in the Columbia River Basin dominated by atmospheric rivers (ARs). In the proposed framework, the historical AR events are identified based on the integrated water vapor transport thresholds used in the AR category scale. The precipitation depths during the identified AR events are then maximized by simultaneously optimizing the AR position and its atmospheric moisture. Finally, the design precipitation sequence is formed by substituting each historical AR event with the corresponding maximized AR event, acting as the basis of long-duration MP. As a result, the maximum 6-month winter period accumulated basin-average precipitation depths: long-duration MP, for the drainage areas of Bonneville Dam and Libby Dam, are estimated to be 961.0 mm and 1101.7 mm, respectively. To the authors’ knowledge, this is the first study estimating the MP for long durations on the order of several months and for very large basins (above 100,000 km2) by using the NWM-based approach.

Evaluation of three approaches to probable maximum precipitation estimation: a study on two Indian river basins

Evaluation of three approaches to probable maximum precipitation estimation: a study on two Indian river basins

Estimating probable maximum precipitation for Bangladesh

In this paper, one-day probable maximum precipitation (PMP) is estimated for 29 meteorological stations of Bangladesh. A widely recognised statistical method, viz. Hershfield method, is used for PMP estimation. Afterward, the spatial prediction map of PMP is generated based on geostatistical analysis. It is found that Hershfield's frequency factor (Km) for estimating PMP varies from 2.03 to 8.03 while most are around 3 to 4. Results indicate that higher values of PMP are found in the eastern part of the country whereas lower at the western part. However, maximum PMP (811 mm) is found in Bhola which is located in the coastal region. The second highest is also found in the coastal region. Results from the geostatistical analysis shows that empirical Bayesian kriging (EBK) performs slightly better in the spatial prediction map generation.

Concept of Threshold in the Estimation of Probable Maximum Precipitation: Hershfield’s Method Revisited

AbstractHershfield’s statistical procedure is recognized by the World Meteorological Organization (WMO) and widely used for estimating probable maximum precipitation (PMP). It uses the frequency fa...

Probable maximum precipitation estimation over western Iran based on remote sensing observations: comparing deterministic and probabilistic approaches

ABSTRACT Reliable estimation of probable maximum precipitation (PMP) is critical to ensure the safety and resilience of communities. The aim of this study is to improve the estimation of 24-h PMP using ground-based and remotely sensed data, particularly over data-scarce regions. Gumbel copula, as a bivariate extreme value distribution based on a moisture maximization method, was applied to estimate PMP. The framework allows us to examine the simultaneous occurrence of extreme precipitable water vapour (PW) and precipitation efficiency (PE) and determines extreme PW values using a regional remote sensing algorithm. This novel framework was compared with conventional methods including the Hershfield and moisture maximization approaches, which do not consider the dependencies between extreme PW and PE. The results demonstrate the importance of considering the dependence structure between extreme PW and PE in the estimation of PMP and the applicability of remotely sensed data, especially for data-scarce regions.

Updating the estimation of 1-day probable maximum precipitation in South Africa

Study regionSouth Africa Study focusThe Probable Maximum Precipitation (PMP) is the theoretical upper limit of extreme rainfall and is widely used by engineers and hydrologists to determine the Probable Maximum Flood (PMF) which is critical for the design and risk management of high-hazard hydraulic structures. In South Africa, the PMP was last estimated over 50 years ago using approximately 30 years of data. Since then numerous severe rainfall events have occurred which exceed presently available PMP estimates. Despite this, the outdated estimates are currently used in professional practice. In addition, modernised methods have been developed and applied globally to estimate the PMP, highlighting the need to update the PMP estimates for South Africa. This paper aims to present updated and modernised PMPs for the country. New hydrological insights for the regionUsing updated rainfall records and a storm maximisation and transposition approach, this paper provides new 1-day PMP estimates for the country. The importance of revising the PMP to include new extreme rainfall events is highlighted as the majority of the events used in this study occurred after the publication of the previous estimates. The use of extended rainfall records and modernised methods produces generally larger PMP estimates compared to the previous estimates and continual revision of the PMP is recommend to include new extreme rainfall events.

Analysis of uncertainty and non-stationarity in probable maximum precipitation in Brazos River basin

Probable Maximum Precipitation (PMP) is used for designing major hydraulic structures, such as dams and reservoirs, nuclear power plants, and flood protection works. However, the estimated PMP values are associated with uncertainties that have received significant attention in recent years, partly because hydrologic extremes are projected to become more frequent, severe, and uncertain with non-stationarity and natural climate variability. This study compared four methods of estimating PMP, ranging from hydrometeorological to statistical, including up-to-date grid based and site-specific in the Brazos River basin (BRB). BRB is the largest river basin in Texas and it contains a range of climates from subtropical arid to subtropical humid. The objective of this study was to quantify the uncertainty associated with PMP estimation in terms of change in the PMP value and emphasize the necessity of including the effect of non-stationarity on PMP. The uncertainty analysis incorporates the effect of three sources of error: (1) PMP estimation method, (2) topography, and (3) non-stationarity. The contribution of each of the uncertainty sources to the 24-hour PMP estimation was quantified and found to be as 53.5% (selection of method), 31.4% (effect of non-stationarity), and 15.1% (effect of topography). The uncertainty of PMP estimation was more sensitive to the existing observation statistics and the selection of method than to the differences between climate zones. Results showed an overall significant increase in 24-hour record precipitation (+19.5 mm) and PMP (+22.3 mm) in BRB between two historical periods 1940–1976 and 1977–2013. Thus, it is concluded that extreme precipitation in BRB showed non-stationarity which affected PMP shift during the historical period.

Analyzing Uncertainty in Probable Maximum Precipitation Estimation With Pseudoadiabatic Assumption

AbstractThis study aimed to evaluate a probable maximum precipitation (PMP) estimation approach using a moisture‐maximization method. This method enables the estimation of precipitable water (PW) using a surface dew point, under a pseudoadiabatic assumption. However, the deviation of the PW (as estimated using the surface dew point) from the actual observed PW mostly leads to an uncertain PMP estimation, as it is difficult to estimate the actual atmospheric moisture content in an air column using the surface dew point alone. In this study, to consider abundant atmospheric data spanning a long‐term period, we employed the reanalysis data from “Japanese 55‐year Reanalysis” (JRA‐55). The data showed good reliability for the surface dew point and PW. To quantify the deviation, we estimated the errors between the actual and estimated PW values for the moisture‐maximization method at 30 points across Japan. Here, the actual PW was extracted directly from JRA‐55, and the estimated PW was obtained using the surface dew point extracted from JRA‐55. We confirmed that the event PW was the largest source of error in the PMP estimation and that the magnitude of the errors was highly correlated with the surface dew point. We analyzed the vertical dew point profile for events with large estimation errors and confirmed that a low surface dew point showed a high deviation in the air column. Therefore, the use of PMP estimations with the moisture‐maximization method should be carefully considered in rainfall events with low surface dew points (e.g., lower than 18°C).