POTENTIAL OF EXTENDING THE RAINFALL INTENSITY–DURATION–FREQUENCY RELATIONSHIP TO NON-RECORDING RAIN GAUGES

Maximum rainfall intensity–duration–frequency (IDF) curves are commonly applied to determine the design rainfall in water resource projects. Normally, the IDF relationship is derived from recording rain gauges. As the network of non-recording rain gauges (daily rainfall) in Taiwan has a higher density than recording rain gauges, attempts were made in this study to extend the IDF relationship to non-recording rain gauges. Eighteen recording rain gauges and 99 non-recording rain gauges over the Chi-Nan area in Southern Taiwan provide the data sets. The regional IDF formulae were generated for ungauged areas to estimate rainfall intensity for various return periods and rainfall durations larger than or equal to one hour. For rainfall durations less than one hour, a set of adjustment formulae were applied to modify the regional IDF formulae. The method proposed in this study had reasonable application to non-recording rain gauges, which was concluded from the verification of four additional recording rain gauges. © 1997 John Wiley & Sons, Ltd.     

Simple generalization approach for intensity–duration–frequency relationships

Rainfall intensity–duration–frequency (IDF) relationships describe rainfall intensity as a function of duration and return period, and they are significant for water resources planning, as well as for the design of hydraulic constructions. In this study, the two‐parameter lognormal (LN2) and Gumbel distributions are used as parent distribution functions. Derivation of the IDF relationship by this approach is quite simple, because it only requires an appropriate function of the mean of annual maximum rainfall intensity as a function of rainfall duration. It is shown that the monotonic temporal trend in the mean rainfall intensity can successfully be described by this parametric function which comprises a combination of the parameters of the quantile function a(T) and completely the duration function b(d) of the separable IDF relationship. In the case study of Aegean Region (Turkey), the IDF relationships derived through this simple generalization procedure (SGP) may produce IDF relationships as successfully as does the well‐known robust estimation procedure (REP), which is based on minimization of the nonparametric Kruskal–Wallis test statistic with respect to the parameters θ and η of the duration function. Because the approach proposed herein is based on lower‐order sample statistics, risks and uncertainties arising from sampling errors in higher‐order sample statistics were significantly reduced. The authors recommend to establish the separable IDF relationships by the SGP for a statistically favorable two‐parameter parent distribution, because it uses the same assumptions as the REP does, it maintains the observed temporal trend in the mean additionally, it is easy to handle analytically and requires considerably less computational effort. Copyright © 2012 John Wiley & Sons, Ltd.     

How to construct future IDF curves,under changing climate,for sites with scarce rainfall records?

Optimal designs of stormwater systems rely very much on the rainfall Intensity–Duration–Frequency (IDF) curves. As climate has shown significant changes in rainfall characteristics in many regions, the adequacy of the existing IDF curves is called for particularly when the rainfall are much more intense. For data sparse sites/regions, developing IDF curves for the future climate is even challenging. The current practice for such regions is, for example, to ‘borrow’ or ‘interpolate’ data from regions of climatologically similar characteristics. A novel (3‐step) Downscaling‐Comparison‐Derivation (DCD) approach was presented in the earlier study to derive IDF curves for present climate using the extracted Dynamically Downscaled data an ungauged site, Darmaga Station in Java Island, Indonesia and the approach works extremely well. In this study, a well validated (3‐step) DCD approach was applied to develop present‐day IDF curves at stations with short or no rainfall record. This paper presents a new approach in which data are extracted from a high spatial resolution Regional Climate Model (RCM; 30 × 30 km over the study domain) driven by Reanalysis data. A site in Java, Indonesia, is selected to demonstrate the application of this approach. Extremes from projected rainfall (6‐hourly results; ERA40 Reanalysis) are first used to derive IDF curves for three sites (meteorological stations) where IDF curves exist; biases observed resulting from these sites are captured and serve as very useful information in the derivation of present‐day IDF curves for sites with short or no rainfall record. The final product of the present‐day climate‐derived IDF curves fall within a specific range, +38% to +45%. This range allows designers to decide on a value within the lower and upper bounds, normally subjected to engineering, economic, social and environmental concerns. Deriving future IDF curves for Stations with existing IDF curves and ungauged sites with simulation data from RCM driven by global climate model (GCM ECHAM5) (6‐hourly results; A2 emission scenario) have also been presented. The proposed approach can be extended to other emission scenarios so that a bandwidth of uncertainties can be assessed to create appropriate and effective adaptation strategies/measures to address climate change and its impacts. Copyright © 2013 John Wiley & Sons, Ltd.     

Selecting the best IDF model by using the multifractal approach

In this work, the multifractal properties of hourly rainfall data recorded at a location in Southern Spain have been related to the scale properties of the corresponding intensity–duration–frequency (IDF) curves. Four parametric models for the IDF curves have been fitted to the quantiles of rainfall obtained using the generalized Pareto frequency distribution function with the extreme data series obtained for the same place. The scaling of the rainfall intensity moments has been analysed, and the empirical moments scaling exponent function has been obtained. The corresponding values of q₁ and γ₁ have been empirical and theoretically calculated and compared with some characteristics of the different IDF models. Thus, the scaling behaviour of IDF curves has been analysed, and the best model has been selected. Copyright © 2012 John Wiley & Sons, Ltd.     

Estimates of changes in design rainfall values for Canada

Annual maximum rainfall data from 51 stations in Canada were analyzed for trends and changes by using the Mann–Kendall trend test and a bootstrap resampling approach, respectively. Rainfall data were analyzed for nine durations ranging from 5 min to 24 h. The data analyzed are typically used in the development of intensity‐duration‐frequency (IDF) curves, which are used for estimating design rainfall values that form an input for the design of critical water infrastructure. The results reveal more increasing than decreasing trends and changes in the data with more increasing changes and larger changes, noted for the longer rainfall durations. The results also indicate that a traditional trend test may not be sufficient when the interest is in identifying changes in design rainfall quantiles. Copyright © 2012 John Wiley & Sons, Ltd.     

Incorporating uncertainty analysis into a regional IDF formula

A rainfall intensity–duration–frequency (IDF) relationship was generated by pooling annual maximum rainfall series from 14 recording rain gauges in southern Taiwan. Dimensionless frequency curves, plotted by the growth curve method, can be well fitted by regression equations for a duration ranging from 10 mins to 24 hours. As the parameters in regression equations have a good statistical relationship with average annual rainfall, a generalized regional IDF formula was then formulated. The formula, based on average annual rainfall as an index, can be easily applied to non-recording rain gauges. This paper further applies the mean value first-order second moment (MFOSM) method to estimate the uncertainty of the proposed regional IDF formula. From a stochastic viewpoint, the generalized regional IDF formula can accurately simulate the IDF relationship developed using frequency analysis (EV1) at individual stations. The method can provide both rainfall intensity and variance isohyetal maps for various rainfall durations and return periods over the study area. © 1998 John Wiley & Sons, Ltd.     

A multiscaling‐based intensity–duration–frequency model for extreme precipitation

Rainfall intensity–duration–frequency (IDF) curves are a standard tool in urban water resources engineering and management. They express how return levels of extreme rainfall intensity vary with duration. The simple scaling property of extreme rainfall intensity, with respect to duration, determines the form of IDF relationships. It is supposed that the annual maximum intensity follows the generalized extreme value (GEV) distribution. As well known, for simple scaling processes, the location parameter and scale parameter of the GEV distribution obey a power law with the same exponent. Although, the simple scaling hypothesis is commonly used as a suitable working assumption, the multiscaling approach provides a more general framework. We present a new IDF relationship that has been formulated on the basis of the multiscaling property. It turns out that the GEV parameters (location and scale) have a different scaling exponent. Next, we apply a Bayesian framework to estimate the multiscaling GEV model and to choose the most appropriate model. It is shown that the model performance increases when using the multiscaling approach. The new model for IDF curves reproduces the data very well and has a reasonable degree of complexity without overfitting on the data.     

Green‐Ampt Curve‐Number mixed procedure as an empirical tool for rainfall–runoff modelling in small and ungauged basins

The Soil Conservation Service Curve Number (SCS‐CN) method is a popular rainfall–runoff model that is widely used to estimate direct runoff from small and ungauged basins. The SCS‐CN is a simple and valuable approach to quantify the total streamflow volume generated by storm rainfall, but its use is not appropriate for estimating the sub‐daily incremental rainfall excess. To overcome this drawback, we propose to include the Green‐Ampt (GA) infiltration model into a mixed procedure, which is referred to as Curve Number for Green‐Ampt (CN4GA), aiming to distribute in time the information provided by the SCS‐CN method. For a given storm, the computed SCS‐CN total net rainfall amount is employed to calibrate the soil hydraulic conductivity parameter of the GA model. The proposed procedure is evaluated by analysing 100 rainfall–runoff events that were observed in four small catchments of varying size. CN4GA appears to provide encouraging results for predicting the net rainfall peak and duration values and has shown, at least for the test cases considered in this study, better agreement with the observed hydrographs than the classic SCS‐CN method. Copyright © 2012 John Wiley & Sons, Ltd.     

Deriving a practical form of IDF formula using transformed rainfall intensities

A general form of formula is presented for the rainfall Intensity–Duration–Frequency (IDF) relationship. This formula is derived from the nearly normal probability distribution function of transformed intensities. In order to transform the raw intensities, a correcting non‐constant spread technique, the Kruskal–Wallis statistic, and the Box–Cox transformation are adopted. These transformations enable to express a simpler model for the IDF formula that agrees well with traditional IDF relationships. Since the proposed method allows the estimation of any percentile value of intensities with a single equation, the intensity percentile at arbitrary duration can be generated easily. The validity of the formula derived by means of the proposed method is assessed using data from major weather stations in Korea. The results show that the percentile intensities produced using the proposed method are in good agreement with those of traditional frequency analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

Trends in rainfall and temperature in the Peruvian Amazon–Andes basin over the last 40 years (1965–2007)

The hydroclimatology of the Peruvian Amazon–Andes basin (PAB) which surface corresponding to 7% of the Amazon basin is still poorly documented. We propose here an extended and original analysis of the temporal evolution of monthly rainfall, mean temperature (T_mean), maximum temperature (T_max) and minimum temperature (T_min) time series over two PABs (Huallaga and Ucayali) over the last 40 years. This analysis is based on a new and more complete database that includes 77 weather stations over the 1965–2007 period, and we focus our attention on both annual and seasonal meteorological time series. A positive significant trend in mean temperature of 0.09 °C per decade is detected over the region with similar values in the Andes and rainforest when considering average data. However, a high percentage of stations with significant T_mean positive trends are located over the Andes region. Finally, changes in the mean values occurred earlier in T_max (during the 1970s) than in T_min (during the 1980s). In the PAB, there is neither trend nor mean change in rainfall during the 1965–2007 period. However, annual, summer and autumn rainfall in the southern Andes presents an important interannual variability that is associated with the sea surface temperature in the tropical Atlantic Ocean while there are limited relationships between rainfall and El Niño‐Southern Oscillation (ENSO) events. On the contrary, the interannual temperature variability is mainly related to ENSO events. Copyright © 2012 John Wiley & Sons, Ltd.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi,Congo, under the hypothesis of inadequate data

Abstract

Intensity–Duration–Frequency (IDF) curves for precipitation constitute a probabilistic tool and have proven useful in water resources management. In particular, IDF curves for precipitation enable questions on the extreme character of precipitation to be answered. The construction of IDF curves for precipitation is difficult or impossible in tropical areas due to the lack of long-term extreme precipitation data. A technique is proposed to overcome this shortcoming by combining limited high-frequency information on rainfall extremes with long-term daily rainfall information. It may be regarded as an extension of Koutsoyiannis' approach. Using this technique, IDF curves for precipitation are produced for Lubumbashi in Congo.

Citation Van de Vyver, H. & Demarée, G. R. (2010) Construction of Intensity–Duration–Frequency (IDF) curves for precipitation at Lubumbashi, Congo, under the hypothesis of inadequate data. Hydrol. Sci. J. 55(4), 555–564.     

Origination of <Emphasis Type="Italic">G</Emphasis> conditions in the ionospheric <Emphasis Type="Italic">F</Emphasis> region depending on solar and geomagnetic activity

The dependence of the origination of G conditions in the ionospheric F region on solar and geomagnetic activity has been determined based on numerical simulation of the ionosphere over points 50° N, 105° E and 70° N, 105° E for summer conditions at noon. It has been found that the threshold value of the Kp geomagnetic activity index (Kp _S ), beginning from which a G condition can originate, is minimal for a low solar activity level at relatively high latitudes during the recovery phase of a geomagnetic storm. On average, Kp _S increases with increasing solar activity, but G conditions can originate at high solar activity levels and be absent at moderate ones for certain Kp values, which was apparently predicted for the first time. These properties of the origination of G conditions do not contradict the known results of a G-condition statistical analysis performed based on the data from the global network of ionospheric stations.     

Effect of spatial variation characteristics on contouring of design storm depth

The ordinary kriging method, a geostatistical interpolation technique, was applied for developing contour maps of design storm depth in northern Taiwan using intensity–duration–frequency (IDF) data. Results of variogram modelling on design storm depths indicate that the design storms can be categorized into two distinct storm types: (i) storms of short duration and high spatial variation and (ii) storms of long duration and less spatial variation. For storms of the first category, the influence range of rainfall depth decreases when the recurrence interval increases, owing to the increasing degree of their spatial independence. However, for storms of the second category, the influence range of rainfall depth does not change significantly and has an average of approximately 72 km. For very extreme events, such as events of short duration and long recurrence interval, we do not recommend usage of the established design storm contours, because most of the interstation distances exceed the influence ranges. Our study concludes that the influence range of the design storm depth is dependent on the design duration and recurrence interval and is a key factor in developing design storm contours. Copyright © 2003 John Wiley & Sons, Ltd.     

Non-crossing nonlinear regression quantiles by monotone composite quantile regression neural network,with application to rainfall extremes

The goal of quantile regression is to estimate conditional quantiles for specified values of quantile probability using linear or nonlinear regression equations. These estimates are prone to “quantile crossing”, where regression predictions for different quantile probabilities do not increase as probability increases. In the context of the environmental sciences, this could, for example, lead to estimates of the magnitude of a 10-year return period rainstorm that exceed the 20-year storm, or similar nonphysical results. This problem, as well as the potential for overfitting, is exacerbated for small to moderate sample sizes and for nonlinear quantile regression models. As a remedy, this study introduces a novel nonlinear quantile regression model, the monotone composite quantile regression neural network (MCQRNN), that (1) simultaneously estimates multiple non-crossing, nonlinear conditional quantile functions; (2) allows for optional monotonicity, positivity/non-negativity, and generalized additive model constraints; and (3) can be adapted to estimate standard least-squares regression and non-crossing expectile regression functions. First, the MCQRNN model is evaluated on synthetic data from multiple functions and error distributions using Monte Carlo simulations. MCQRNN outperforms the benchmark models, especially for non-normal error distributions. Next, the MCQRNN model is applied to real-world climate data by estimating rainfall Intensity–Duration–Frequency (IDF) curves at locations in Canada. IDF curves summarize the relationship between the intensity and occurrence frequency of extreme rainfall over storm durations ranging from minutes to a day. Because annual maximum rainfall intensity is a non-negative quantity that should increase monotonically as the occurrence frequency and storm duration decrease, monotonicity and non-negativity constraints are key constraints in IDF curve estimation. In comparison to standard QRNN models, the ability of the MCQRNN model to incorporate these constraints, in addition to non-crossing, leads to more robust and realistic estimates of extreme rainfall.     

Extreme precipitation time trends in Ontario, 1960–2010

The impact of climate change on the behaviour of intensity–duration–frequency curves is critical to the estimation of design storms, and thus to the safe design of drainage infrastructure. The present study develops a regional time trend methodology that detects the impact of climate change on extreme precipitation from 1960 to 2010. The regional time trend linear regression method is fitted to different durations of annual maximum precipitation intensities derived from multiple sites in Ontario, Canada. The results show the relationship between climate change and increased extreme precipitation in this province. The regional trend analysis demonstrates, under nonstationary conditions arising from climate change, that the intensity of extreme precipitation increased decennially between 1.25% for the 30‐min storm and 1.82% for the 24‐h storm. A comparison of the results with a regional Mann–Kendall test validates the found regional time‐trend results. The results are employed to extrapolate the intensity–duration–frequency curves temporally and spatially for future decades across the province. The results of the regional time trend assessment help with the establishment of new safety margins for infrastructure design in Ontario. Copyright © 2016 John Wiley & Sons, Ltd.     

Comparison of methods for applying the Priestley–Taylor equation at a regional scale

The scenario assumed for this study was that of a region with a complete or first‐order weather station surrounded by a network of second‐order stations, where only monthly air temperature data were available. The objective was to evaluate procedures to estimate the monthly α parameter of the Priestley–Taylor equation in the second‐order stations by adjusting and extrapolating α values determined at the first‐order station. These procedures were applied in two climatic zones of north‐east Spain with semi‐arid continental and semi‐arid Mediterranean climates, respectively. Procedure A assumed α to be constant over each zone for each month (direct extrapolation). Procedure B accounted for differences in vapour pressure deficit and available energy for evapotranspiration between the first‐ and second‐order stations. Procedure C was based on equating the Penman–Monteith (P–M) and Priestley–Taylor (P–T) equations on a monthly basis to solve for α. Methods to estimate monthly mean vapour pressure deficit, net radiation and wind speed were developed and evaluated. A total of 11 automated first‐order weather stations with a minimum period of record of 6 years (ranging from 6 to 10 years) were used for this study. Six of these stations were located in the continental zone and five in the Mediterranean zone. One station in each zone was assumed to be first‐order whereas the remainder were taken as second‐order stations. Monthly α parameters were calibrated using P–M reference crop evapotranspiration (ET₀) values, calculated hourly and integrated for monthly periods, which were taken as ‘true’ values of ET₀. For the extrapolation of monthly α parameters, procedure A was found to perform slightly better than procedure B in the Mediterranean zone. The opposite was true in the continental zone. Procedure C had the worst performance owing to the non‐linearity of the P–M equation and errors in the estimation of monthly available energy, vapour pressure deficit and wind speed. Procedures A and B are simpler and performed better. Overall, monthly P–T ET₀ estimates using extrapolated α parameters and R_n?G values were in a reasonable agreement with P–M ET₀ calculated on an hourly basis and integrated for monthly periods. The methods presented for the spatial extrapolation of monthly available energy, vapour pressure deficit and wind speed from first‐ to second‐order stations could be useful for other applications. Copyright © 2001 John Wiley & Sons, Ltd.     

Development of isopluvial map using L-moment approach for Tehri-Garhwal Himalaya

Estimation of design rainfall intensity is crucial for design and planning of water resources engineering projects. The intent of the present study is to develop regional IDF curves for Tehri-Garhwal Himalayan region in India, wherein numbers of hydropower projects are in planning and execution stage. Self Recording Rain Gauge (SRRG) stations are generally not so frequent in the project locations. Under this situation, the engineers are forced to use regional intensity duration frequency (IDF) curves. Under this study, four stations viz. Tehri M.T.Lab, Mukhim, Pilkhi and Dhuttu were available with SRRG data. These data are used to develop the regional IDF curve for entire Tehri-Garwal region. After selection of the most intensive storms, return periods has been determined using regionalized L-moment method. After developing IDF curves for above four raingauge stations, Thiessen Ploygon method is applied to find out average IDF curve. To show the spatial variability, Isopluvial maps have been generated using ArcGIS and a relation equation has been developed.     

A simple temperature method for the estimation of evapotranspiration

Accurate estimation of evapotranspiration (ET) is essential in water resources management and hydrological practices. Estimation of ET in areas, where adequate meteorological data are not available, is one of the challenges faced by water resource managers. Hence, a simplified approach, which is less data intensive, is crucial. The FAO‐56 Penman–Monteith (FAO‐56 PM) is a sole global standard method, but it requires numerous weather data for the estimation of reference ET. A new simple temperature method is developed, which uses only maximum temperature data to estimate ET. Ten class I weather stations data were collected from the National Meteorological Agency of Ethiopia. This method was compared with the global standard PM method, the observed Piche evaporimeter data, and the well‐known Hargreaves (HAR) temperature method. The coefficient of determination (R²) of the new method was as high as 0.74, 0.75, and 0.91, when compared with that of PM reference evapotranspiration (ET_o), Piche evaporimeter data, and HAR methods, respectively. The annual average R² over the ten stations when compared with PM, Piche, and HAR methods were 0.65, 0.67, and 0.84, respectively. The Nash–Sutcliff efficiency of the new method compared with that of PM was as high as 0.67. The method was able to estimate daily ET with an average root mean square error and an average absolute mean error of 0.59 and 0.47 mm, respectively, from the PM ET_o method. The method was also tested in dry and wet seasons and found to perform well in both seasons. The average R² of the new method with the HAR method was 0.82 and 0.84 in dry and wet seasons, respectively. During validation, the average R² and Nash–Sutcliff values when compared with Piche evaporation were 0.67 and 0.51, respectively. The method could be used for the estimation of daily ET_o where there are insufficient data. Copyright © 2013 John Wiley & Sons, Ltd.