Intensity-duration-frequency Curves Research Articles

Rainfall Intensity-Duration-Frequency Relationship. Case Study: Depth-Duration Ratio in a Semi-Arid Zone in Mexico

Intensity–Duration–Frequency (IDF) curves describe the relationship between rainfall intensity, rainfall duration, and return period. They are commonly used in the design, planning and operation of hydrologic, hydraulic, and water resource systems. Considering the intense rainfall presence with flooding occurrences, limited data used to develop IDF curves, and importance to improve the IDF design for the Ensenada City in Baja California, this research study aims to investigate the use and combinations of pluviograph and daily records, to assess rain behavior around the city, and select a suitable method that provides the best results of IDF relationship, consequently updating the IDF relationship for the city for return periods of 10, 25, 50, and 100 years. The IDF relationship is determined through frequency analysis of rainfall observations. Also, annual maximum rainfall intensity for several duration and return periods has been analyzed according to the statistical distribution of Gumbel Extreme Value (GEV). Thus, Chen’s method was evaluated based on the depth-duration ratio (R) from the zone, and the development of the IDF relationship for the rain gauges stations was focused on estimating the most suitable (R) ratio; chosen from testing several methods and analyzing the rain in the region from California and Baja California. The determined values of the rain for one hour and return period of 2 years (P12) obtained were compared to the values of some cities in California and Baja California, with a range between 10 and 16.61 mm, and the values of the (R) ratio are in a range between 0.35 and 0.44; this range is close to the (R) ratio of 0.44 for one station in Tijuana, a city 100 km far from Ensenada. The values found here correspond to the rainfall characteristics of the zone; therefore, the method used in this study can be replicated to other semi-arid zones with the same rain characteristics. Finally, it is suggested that these results of the IDF relationship should be incorporated on the Norm of the State of Baja California as the recurrence update requires it upon recommendation. This study is the starting point to other studies that imply the calculation of a peak flow and evaluation of hydraulic structures as an input to help improve flood resilience in the city of Ensenada.

A Robust Method to Update Local River Inundation Maps Using Global Climate Model Output and Weather Typing Based Statistical Downscaling

Global warming is changing the magnitude and frequency of extreme precipitation events. This requires updating local rainfall intensity-duration-frequency (IDF) curves and flood hazard maps according to the future climate scenarios. This is, however, far from straightforward, given our limited ability to model the effects of climate change on the temporal and spatial variability of rainfall at small scales. In this study, we develop a robust method to update local IDF relations for sub-daily rainfall extremes using Global Climate Model (GCM) data, and we apply it to a coastal town in NW Spain. First, the relationship between large-scale atmospheric circulation, described by means of Lamb Circulation Type classification (LCT), and rainfall events with potential for flood generation is analyzed. A broad ensemble set of GCM runs is used to identify frequency changes in LCTs, and to assess the occurrence of flood generating events in the future. In a parallel way, we use this Weather Type (WT) classification and climate-flood linkages to downscale rainfall from GCMs, and to determine the IDF curves for the future climate scenarios. A hydrological-hydraulic modeling chain is then used to quantify the changes in flood maps induced by the IDF changes. The results point to a future increase in rainfall intensity for all rainfall durations, which consequently results in an increased flood hazard in the urban area. While acknowledging the uncertainty in the GCM projections, the results show the need to update IDF standards and flood hazard maps to reflect potential changes in future extreme rainfall intensities.

Simulating rainfall IDF curve for flood warnings in the Ca Mau coastal area under the impacts of climate change

Purpose The purpose of this study is to evaluate the rainfall intensities and their limits for durations from 0.25 to 8 h with return periods from 2 to 100 years for Ca Mau City in Vietnam. Design/methodology/approach First, the quality of the historical rainfall data series in 44 years (1975–2018) at Ca Mau station was assessed using the standard normal homogeneity test and the Pettitt test. Second, the appraised rainfall data series are used to establish the rainfall intensity-duration-frequency curve for the study area. Findings Based on the findings, a two-year return period, the extreme rainfall intensities (ERIs) ranged from 9.1 mm/h for 8 h rainstorms to 91.2 mm/h for 0.25 h. At a 100-year return period, the ERIs ranged from 18.4 mm/h for 8 h rainstorms to 185.8 mm/h for 0.25 h. The results also show that the narrowest uncertainty level between the lower and upper limits recorded 1.6 mm at 8 h for the two-year return period while the widest range is at 42.5 mm at 0.25 h for the 100-year return period. In general, the possibility of high-intensity rainfall values compared to the extreme rainfall intensities is approximately 2.0% at the 100-year return period. Originality/value The results of the rainfall IDF curves can provide useful information for policymakers to make the right decisions in controlling and minimizing flooding in the study area.

Development of Intensity Duration Frequency (IDF) Curves for Rainfall Prediction within the Middle Niger River Basin

Rainfall Intensity-Duration-Frequency (IDF) relationship remains one of the mostly used tools in hydrology and water resources engineering, especially for planning, design and operations of water resource projects. IDF relationship can provide adequate information about the intensity of rainfall at different duration for various return periods. The focus of this research was to develop IDF curves for the prediction of rainfall intensity within the middle Niger River Basin (Lokoja and Ilorin) using annual maximum daily rainfall data. Forty (40) year’s annual maximum rainfall data ranging from 1974 to 2013 was employed for the study. To ascertain the data quality, selected preliminary analysis technique including; descriptive statistics, test of homogeneity and outlier detection test were employed. To compute the three hours rainfall intensity, the ratio of rainfall amount and duration was used while the popular Gumbel probability distribution model was employed to calculate the rainfall frequency factor. To assess the best fit model that can be employed to predict rainfall intensity for various return periods at ungauged locations, four empirical IDF equations, namely; Talbot, Bernard, Kimijima and Sherman equations were employed. The model with the least calculated sum of minimized root mean square error (RMSE) was adopted as the best fit empirical model. Results obtained revealed that the Talbot model was the best fit model for Ilorin and Lokoja with calculated sum of minimized error of 1.32170E-07 and 8.953636E-08. This model was thereafter employed to predict the rainfall intensity for different durations at 2, 5, 10, 25, 50 and 100yrs return periods respectively.

On the Rainfall Intensity–Duration–Frequency Curves, Partial-Area Effect and the Rational Method: Theory and the Engineering Practice

This research evaluates the partial-area effect and its relationship with the rainfall intensity–duration–frequency (IDF) equations. In the Rational Method, if the critical rainfall duration is shorter than the time of concentration, the partial-area effect occurs. We proved that the partial area could exist for the general ID equation i=a/(b+td)c, only when c>1. For these equations, in the application of the Rational Method, the maximum discharge at basin outlet occurs for rainfall duration (td) equal to b/(c−1). Nevertheless, for that case, the Depth Duration Frequency (DDF) has a maximum at that rainfall duration. These situations are present in engineering practice and will be discussed in this paper. Research was done to look for IDF equations with c>1 in hydrologic engineering practice. It found 640 inconsistent IDF equations (c>1) in four countries (Brazil, Mexico, India, and USA), which means that a fundamental principle for building consistent IDF equations (i.e., c>1), published in the scientific literature since 1998, did not reach the hydrologic engineering practice fully. We provided some analysis regarding this gap between theory and engineering practice.

Addressing uncertainty in extreme rainfall intensity for semi-arid urban regions: case study of Delhi, India

Classical approaches are used to develop rainfall intensity duration frequency curves for the estimation of design rainfall intensities corresponding to various return periods. The study modelled extreme rainfall intensities at different durations and compared the classical Gumbel and generalized extreme value (GEV) distributions in semi-arid urban region. The model and parameter uncertainties are translated to uncertainties in design storm estimates. A broader insight emerges that rainfall extremes in 1 h and 3 h are sensitive to the choice of frequency analysis (GEV in this case) and helps address anticipated intensification of extreme events for short duration at urban local scale. In comparison with Gumbel, GEV predicts higher extreme rainfall intensity corresponding to various return periods and duration (for 1-h duration the increase in extreme rainfall intensity is from 27 to 33% for return periods 10 years and higher, 3-h and 50-year return period—20%, 3-h and 100-year return period—20.6%, 24 h at similar return periods—10%). The Bayesian posterior distribution has a calibration effect on the GEV predictions and reduces the upper range of uncertainty in the GEV probability model prediction from a range of 16–31% to 10–28.4% for return period varying from 10 to 50 year for 1-h storms. In geographically similar areas these extreme intensities may be used to prepare for the rising flash flood risks.

Formulasi Intensitas Hujan dan Kurva Intensitas Durasi Frekuensi (IDF) yang Sesuai pada Wilayah Hulu Kota Batu, Provinsi Jawa Timur

Intensitas hujan merupakan masukan yang sangat penting dalam pekerjaan sumber daya air terutama terkait dengan banjir, erosi, dan tanah longsor. Kejadian banjir bandang yang pernah terjadi di wilayah studi (hulu Kota Batu) merupakan dampak dari masifnya perubahan tutupan lahan dan tingginya intensitas hujan yang terjadi. Kegiatan yang bersifat antisipasi and mitigasi banjir membutuhkan dukungan data hujan yang berkualitas. Studi ini bertujuan untuk mendapatkan rumus empiris yang sesuai untuk memperkirakan intensitas hujan serta kurva Intensitas Durasi Frekuensi (IDF). Metode empiris yang digunakan meliputi Sherman, Ishiguro dan Haspers, sedangkan intensitas hujan rancangan diperoleh dari perhitungan analisa frekuensi dengan berbagai kala ulang. Penentuan metode terpilih dilakukan dengan membandingkan intensitas hujan pengamatan dengan hasil metode empiris berdasarkan nilai koefisien Nash Sutcliffe Efficiency (NSE), kesalahan relatif, dan nilai deviasi yang terjadi. Hasil studi menunjukkan bahwa metode Sherman memiliki kesesuaian yang paling tinggi yang diindikasikan dengan nilai NSE sebesar 0,97, nilai kesalahan relatif kecil 6,59% dan nilai deviasi sebesar 2,56. Untuk mengetahui keandalan metode terpilih, maka dilakukan validasi antara intensitas hujan berdasarkan peluang kala ulang dengan intensitas metode terpilih (Sherman). Hasil validasi menunjukkan metode Sherman memiliki keandalan yang baik dalam memperkirakan intensitas hujan sehingga dapat digunakan untuk mengestimasi intensitas hujan pada wilayah studi.

A new approach to explore climate change impact on rainfall intensity–duration–frequency curves

Increasing the concentration of CO2 and other greenhouse gases in the atmosphere makes a large-scale change in atmospheric processes. Among the most dramatic effects of climate change, its impact on the type, amount, and intensity of rainfall is of particular importance. The goal of the present study was to provide a new method to investigate climate change impacts on rainfall intensity—duration—frequency (IDF) in the southwest of Iran. For this purpose, IDF curves were determined using recorded short-term rainfall from 15 stations. Then, the efficiency of the scale invariance theory was evaluated in determining IDFs by comparing IDFs resulting from observed data and IDFs estimated from the scaling model. Results demonstrated that two sets of IDFs had a good coincidence. In the next step, the data from three RCM models of the CORDEX project under two scenarios (RCP4.5 and RCP8.5) were used, and daily rainfall was downscaled by the musica package. Finally, IDFs were determined for two future periods including 2025–2049 as near future and 2075–2099 as far future. The result showed that rainfall intensity decreased in the north and central parts of the region.

Evaluating intensity-duration-frequency (IDF) curves of satellite-based precipitation datasets in Peninsular Malaysia

In recent years the use of remotely sensed precipitation products in hydrological studies has become increasingly common. The capability of the products in producing rainfall intensity-duration-frequency (IDF) relationships, however, has not been examined in any great detail. The performance of four remote-sensing-based gridded rainfall data processing algorithms (GSMaP_NRT, GSMaP_GC, PERSIANN and TRMM_3B42V7) was evaluated to determine the ability to generate reliable IDF curves. The work was undertaken in Peninsular Malaysia. The best-fitted probability distribution functions (PDFs) of rainfall totals for different durations were used to generate the IDF curves. The accuracy of the gridded IDF curves was evaluated by comparing observed versus estimated IDF curves at 80 locations. The results revealed that a generalized extreme value (GEV) distribution had the best fit to the rainfall intensity for different durations at 62% of the stations, and this was then used to develop the IDF curves. A comparison of these remote sensing derived IDF curves with the observed IDF data revealed that the GSMaP_GC product performed best. In general, the satellite-based precipitation products tended to underestimate the IDF curves. The GSMaP_GC IDF curves were found to be the least biased (8%–27%) compared to the TRMM_3B42V7 IDF curves (65%–67%). The biases in rainfall intensity of different return periods for GSMaP_GC for all grid points were estimated. These results can be used in designing hydraulic structures where gauged data are unavailable.

Update of intensity–duration–frequency curves for Kuwait due to extreme flash floods

Flash floods have devastating power due to their high rainfall intensities and short durations, causing serious damage to infrastructure and human life. Recent observations in the desert environment of Kuwait witnessed an increase in rainfall extremes, and the currently adopted intensity–duration–frequency (IDF) curves constructed three decades ago did not produce reliable design frequencies for existing stormwater drainage systems in residential areas. In this study, the IDF curves for the urban zone of the State of Kuwait were updated with recent records of annual maximum rainfall intensity from January 2006 to December 2017, and the Extreme Value type-I probability distribution was implemented to perform frequency analysis and estimate the design storm. The study concluded that frequent updating of IDF curves is necessary for the examined rainfall data to account for harmonic climatic variations in compliance with sunspot cycles. The updated IDF curves confirmed the pronounced increase in rainfall intensities within short durations of 5–15 min, thereby affecting water-related infrastructure in small urban catchments. Here we call for urgent action to be taken to adopt flood mitigation plans in residential areas to avoid the catastrophic impacts of extreme flash floods.

Evaluation of Design Storms and Critical Rainfall Durations for Flood Prediction in Partially Urbanized Catchments

This study investigates and compares several design storms for flood estimation in partially urbanized catchments. Six different design storms were considered: Euler II, alternating block method, average variability method, Huff’s curves, and uniform rainfall. Additionally, two extreme historical storms were included for comparison. A small, ungauged, partially urbanized catchment in Novigrad (Croatia) was chosen as a study area to account for the infiltration impact on the rainfall-runoff process. The performance of each design storm was assessed based on the flood modeling results, namely the water depth, water velocity, flow rate, and overall flood extent. Furthermore, several rainfall durations were considered to identify a critical scenario. The excess rainfall was computed using the Soil Conservation Service’s Curve Number method, and two-dimensional flooding simulations were performed by the HEC-RAS model. The results confirmed that the choice of the design storm and the rainfall duration has a significant impact on the flood modeling results. Overall, design storms constructed only from IDF curves overestimated flooding in comparison to historical events, whereas design storms derived from the analysis of observed temporal patterns matched or slightly underestimated the flooding results. Of the six considered design storms, the average variability method showed the closest agreement with historical storms.

Climate change and its influence on design rainfall at-site in New South Wales State, Australia

AbstractQuantification of rainfall is needed for planning, designing and operation of water engineering projects. Although there is lot of research on design rainfall in the literature, there is a lack of research considering the impact of climate change on design rainfall. This study focuses on the assessment of the impact of climate changes on design rainfall using data from New South Wales (NSW), Australia. Future stationary and non-stationary intensity–frequency–duration (IFD) curves have been estimated using generalized extreme value (GEV) distribution. The maximum-likelihood estimation method is employed to estimate the parameters of the GEV models. It has been found that the consideration of the climatic change on the rainfall data of the selected station confirms that the simulation exhibits non-stationary behaviour on the IFD curve data. In addition, the results show that when the future period increases, the relative differences between the stationary and non-stationary IFD curves generally increase. Comparison of the new IFD curves estimated in this study with the Australian Rainfall and Runoff (ARR) IFD curves demonstrates that there is a better match between the ARR IFD curves and the new stationary IFD curves compared with the non-stationary IFD curves.

Detecting Rainfall Trend and Development of Future Intensity Duration Frequency (IDF) Curve for the State of Kelantan

Due to global warming, the existing IDF curves that were derived from historical data may no longer valid for estimating future rainfall. On the other hand, the alternative future rainfall data generated from Community Climate System Model version 3 (CCSM3) cannot be used directly due to systematic biases caused by non-inclusion of local features. Quantile mapping was used to bias correct the rainfall data generated by CCSM3 model based on the properties of observed rainfall. Only 4 out of 16 stations in the state of Kelantan have shown an increasing significant trend for 1-h annual maximum rainfall. The best transfer function used to correct bias in CCSM3 data is the second order polynomial function. The quantile mapping for bias correction is satisfactory as the highest RMSE was only 4.045, a reduction by 15% compared to the original CCSM3 data. Subsequently, a unique transfer function was developed to represent the behavior of CCSM3 and observed data for each station. The future intensity was found to increase for short and medium return periods of 2-, 5-, 10- and 25-year, where most of the stations have Climate Change Factor (CCF) larger than 1. On the contrary, for a longer return period of 50- and 100-year, the intensities are predicted to be lower.

Analysis of rainfall intensity-duration-frequency (IDF) curves of Baghdad city

An appropriate formula of rainfall data is the Intensity Duration Frequency (IDF) relationship. The rainfall IDF relationship is one of the tools used considerably in water resources engineering, either in planning, designing and operating projects of water resources, or in flood control projects. The purpose of this paper is to update rainfall IDF curves of Baghdad city developed in previously. The frequency analysis of available rainfall data is perform by three statistical methods, namely, the Gumbel Distribution Theory, the Log Pearson Type III and Log Normal Distribution to attain rainfall intensities for various short durations (0.25, 0.5, 1, 2, 3, 6, 12 and 24) in hours and return periods (2, 5, 10, 25, 50 and 100) in years. IDF equation was derived based on Bernard equation and the results of three distributions were compared using Kolmogorov-Smirnov goodness of fit test with help of the Easy fit software 5.6. The results of three methods were close and accepted at 10% significant level. The maximum rainfall intensity of 118.052mm/hr was happened at the duration 0.25hr of the return period 100yr, whereas the minimum rainfall intensity of 1.257mm/hr was happened at the duration 24hr of the return period 2yr.

Climate change impact on short-duration extreme precipitation and intensity–duration–frequency curves over Europe

To build future climate-proof water systems and to reduce the failure risk of infrastructure, short-duration extreme precipitation design storms must be updated. However, a robust future projection of such storms on a continental scale has not been presented due to the scarcity of long, high quality sub-daily data both for observations and model simulations. To address this need, we develop current and future precipitation intensity–duration–frequency (IDF) curves for Europe for 0.5-, 1-, 3-, 6-, 12- and 24-hour durations and for different return periods ranging between 1 and 100 years derived from a Generalized Pareto Distribution (GPD). Future IDF curves are developed in the framework of the quantile perturbation downscaling method by applying climate change signals from the EURO-CORDEX RCMs on current IDF curves obtained from high-resolution remote sensing based products. Here we show that rarer sub-daily extreme precipitation events will intensify more than less rare events and that changes may depend on precipitation duration. The frequency of sub-daily extreme precipitation events of 50- and 100-year return periods will be tripled under the high-end RCP8.5 scenario. Such intensification will lead to a substantial uplift (16–27% depending on duration and return period) and steepening (17–25% depending on return period) of the IDF curves under future climate change, calling attention to the vulnerability of the existing water infrastructure systems.

Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

Quantitative assessment of annual maxima, peaks-over-threshold and multifractal parametric approaches in estimating intensity-duration-frequency curves from short rainfall records

The present study uses hourly rainfall measurements from 36 raingauge stations in the northeastern United States with more than 55 years of recordings, to assess the accuracy and robustness of three conceptually different parametric approaches to produce intensity-duration-frequency (IDF) curves from rainfall records: (a) the well celebrated parametric IDF model based on annual maxima (AM) series, initially introduced by Rossi and Villani (1994) and later extended by Koutsoyiannis et al. (1998), (b) a peaks-over-threshold (PoT) model based on proper fitting of a reparametrized generalized Pareto (GP) distribution to the scaled excesses of the average rainfall intensity over various durations d, and (c) the analytical approximation introduced by Langousis et al. (2009) for estimation of multifractal (MF) rainfall maxima. Since its development, the third approach has never been tested in real world applications, and/or compared to routinely used approaches for IDF curve estimation. The obtained results show that the MF approach may constitute an important tool for hydrological applications, as it produces more accurate and robust IDF estimates than the other two approaches, irrespective of the duration d and return period T of interest, especially in cases where rainfall records exhibit significant length limitations. In addition, the parameters of the MF analytical approximation are found to be descriptive of the local topography and rainfall climatology of the region, providing a physically meaningful modeling setting that is particularly suited for regional frequency analysis and IDF estimation at ungauged locations.

A Probabilistic Approach for Characterization of Sub-Annual Socioeconomic Drought Intensity-Duration-Frequency (IDF) Relationships in a Changing Environment

Changes in climate, land use, and population can increase annual and interannual variability of socioeconomic droughts in water-scarce regions. This study develops a probabilistic approach to improve characterization of sub-annual socioeconomic drought intensity-duration-frequency (IDF) relationships under shifts in water supply and demand conditions. A mixture Gamma-Generalized Pareto (Gamma-GPD) model is proposed to enhance characterization of both the non-extreme and extreme socioeconomic droughts. Subsequently, the mixture model is used to determine sub-annual socioeconomic drought intensity-duration-frequency (IDF) relationships, return period, amplification factor, and drought risk. The application of the framework is demonstrated for the City of Fort Collins (Colorado, USA) water supply system. The water demand and supply time series for the 1985–2065 are estimated using the Integrated Urban water Model (IUWM) and the Soil and Water Assessment Tool (SWAT), respectively, with climate forcing from statistically downscaled CMIP5 projections. The results from the case study indicate that the mixture model leads to enhanced estimation of sub-annual socioeconomic drought frequencies, particularly for extreme events. The probabilistic approach presented in this study provides a procedure to update sub-annual socioeconomic drought IDF curves while taking into account changes in water supply and demand conditions.

Stochastic seasonal rainfall simulation model for Irbid region, Northern Jordan

ABSTRACT A stochastic hourly simulation model is developed for the synthesis of the rainfall pattern in the northern part of Jordan. The generation of synthetic rainfall data is an attempt to provide longer data sequences. The simulation model is based on statistical properties of rainfall data for three stations in the Northern region of Jordan for the period 1975–2004. The mean and variances of important rainfall characteristics were reasonably well preserved in the synthesized data. The simulated characteristics include the duration, total depth and depth at 50% duration and mass curves of the storms. The intensity-duration-frequency curves generated by this model compared well with locally available curves. The resulting IDF curves based on the stochastically generated storm sequences are usually used for flood estimation in urban/rural watersheds. Using the resulting IDF curves is highly recommended for rigorous, efficient and safe design of hydraulic structures and flood protection works.

Web-Based Tool for the Development of Intensity Duration Frequency Curves under Changing Climate at Gauged and Ungauged Locations

Rainfall Intensity–Duration–Frequency (IDF) curves are among the most essential datasets used in water resources management across the globe. Traditionally, they are derived from observations of historical rainfall, under the assumption of stationarity. Change of climatic conditions makes use of historical data for development of IDFs for the future unreliable, and in some cases, may lead to underestimated infrastructure designs. The IDF_CC tool is designed to assist water professionals and engineers in producing IDF estimates under changing climatic conditions. The latest version of the tool (Version 4) provides updated IDF curve estimates for gauged locations (rainfall monitoring stations) and ungauged sites using a new gridded dataset of IDF curves for the land mass of Canada. The tool has been developed using web-based technologies and takes the form of a decision support system (DSS). The main modifications and improvements between version 1 and the latest version of the IDF_CC tool include: (i) introduction of the Generalized Extreme value (GEV) distribution; (ii) updated equidistant matching algorithm (QM); (iii) gridded IDF curves dataset for ungauged location and (iv) updated Climate Models.