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Observed and simulated densities of wet and dry spells in 1st and 2nd rows (increasing spell length from left to right) with S-MOF, MOF and MOF* in Italy. Bars denote the mean of all sites and the 50 simulation runs.
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Study region: This study focuses on two study areas: the Province of Trento (Italy; 6200 km²), and entire Sweden (447000km²). The Province of Trento is a complex mountainous area including subarctic, humid continental and Tundra climates. Sweden, instead, is mainly dominated by a subarctic climate in the North and an oceanic climate in the South.
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... better understand the performance in the simulation of dry and wet spells, we also plotted their observed and simulated density. Fig. 5 shows the results for Italy and all three algorithms (full network up to a spell duration of 24 h). The patterns for all algorithms are similar. Longer wet spells tend to be underestimated, while longer dry spells tend to be overestimated. Important to notice is the similar performance of S-MOF compared to MOF and MOF*. Its ability to ...
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... importantly, the joint disaggregation has a significant impact on the performance of the precipitation and temperature specific statistics already shown in Figs. 2, 3, 7 and 8. A noticeable decrease in the performance when conducting a joint dis- aggregation in Italy can be depicted from Fig. 10 (precipitation) and Fig. S5 in the Supplementary Material (temperature), which show the MAE from both disaggregation strategies in Italy. For the precipitation (Fig. 10), almost all metrics suffer from a joint ...
Citations
... A widely used method is the non-parametric method of fragments (MOF), where the disaggregation scheme for any target day is obtained from the high-resolution temporal (and spatial, if relevant) structure of a given analogue day selected in the archive of observations (e.g. Mezghani and Hingray, 2009;Breinl and Di Baldassarre, 2019;Park and Chung, 2020;Acharya et al., 2022). By construction, MOF methods preserve the sub-daily patterns of precipitation and the intermittency properties within each day. ...
Analytical multiplicative random cascades (MRCs) are widely used for the temporal disaggregation of coarse-resolution precipitation time series. This class of models applies scaling models to represent the dependence of the cascade generator on the temporal scale and the precipitation intensity. Although determinant, the dependence on the external precipitation pattern is usually disregarded in the analytical scaling models. Our work presents a unified MRC modelling framework that allows the cascade generator to depend in a continuous way on the temporal scale, precipitation intensity and a so-called precipitation asymmetry index. Different MRC configurations are compared for 81 locations in Switzerland with contrasted climates. The added value of the dependence of the MRC on the temporal scale appears to be unclear, unlike what was suggested in previous works. Introducing the precipitation asymmetry dependence into the model leads to a drastic improvement in model performance for all statistics related to precipitation temporal persistence (wet–dry transition probabilities, lag-n autocorrelation coefficients, lengths of dry–wet spells). Accounting for precipitation asymmetry seems to solve this important limitation of previous MRCs. The model configuration that only accounts for the dependence on precipitation intensity and asymmetry is highly parsimonious, with only five parameters, and provides adequate performances for all locations, seasons and temporal resolutions. The spatial coherency of the parameter estimates indicates a real potential for regionalisation and for further application to any location in Switzerland.
... Weather generators generate synthetic sequences of hourly weather variables by using random number generators that match statistics (Ailliot et al., 2015;Mezghani and Hingray, 2009). Various statistical methods exist for temporal disaggregation of daily climate data, ranging from simple interpolations or deterministic approaches to non-parametric approaches and methods that derive statistical relationships from historical data or look for climate analogues (Bennett et al., 2020;Breinl and Di Baldassarre, 2019;Chen, 2016;Debele et al., 2007;Förster et al., 2016;Görner et al., 2021;Liston and Elder, 2006;Park and Chung, 2020;Verfaillie et al., 2017; Poschlod et al., 2018;Zhao et al., 2021). Each of these methods has its own advantages and limitations, and the choice of method depends on factors such as the specific needs of the impact assessment, the quality of the available data, and the computational resources. ...
Climate models provide the required input data for global or regional climate impact analysis in temporally aggregated form, often in daily resolution to save space on data servers. Today, many impact models work with daily data; however, sub-daily climate information is becoming increasingly important for more and more models from different sectors, such as the agricultural, water, and energy sectors. Therefore, the open-source Teddy tool (temporal disaggregation of daily climate model data) has been developed to disaggregate (temporally downscale) daily climate data to sub-daily hourly values. Here, we describe and validate the temporal disaggregation, which is based on the choice of daily climate analogues. In this study, we apply the Teddy tool to disaggregate bias-corrected climate model data from the Coupled Model Intercomparison Project Phase 6 (CMIP6). We choose to disaggregate temperature, precipitation, humidity, longwave radiation, shortwave radiation, surface pressure, and wind speed. As a reference, globally available bias-corrected hourly reanalysis WFDE5 (WATCH Forcing Data methodology applied to ERA5) data from 1980–2019 are used to take specific local and seasonal features of the empirical diurnal profiles into account. For a given location and day within the climate model data, the Teddy tool screens the reference data set to find the most similar meteorological day based on rank statistics. The diurnal profile of the reference data is then applied on the climate model. The physical dependency between variables is preserved, since the diurnal profile of all variables is taken from the same, most similar meteorological day of the historical reanalysis dataset. Mass and energy are strictly preserved by the Teddy tool to exactly reproduce the daily values from the climate models. For evaluation, we aggregate the hourly WFDE5 data to daily values and apply the Teddy tool for disaggregation. Thereby, we compare the original hourly data with the data disaggregated by Teddy. We perform a sensitivity analysis of different time window sizes used for finding the most similar meteorological day in the past. In addition, we perform a cross-validation and autocorrelation analysis for 30 globally distributed samples around the world that represent different climate zones. The validation shows that Teddy is able to reproduce historical diurnal courses with high correlations >0.9 for all variables, except for wind speed (>0.75) and precipitation (>0.5). We discuss the limitations of the method regarding the reproduction of precipitation extremes, interday connectivity, and disaggregation of end-of-century projections with strong warming. Depending on the use case, sub-daily data provided by the Teddy tool could make climate impact assessments more robust and reliable.
... been obtained, it is interesting to go down to hourly and subhourly detail in order to relate the data obtained to hydraulic/ hydrological simulation tools. To this end, statistical temporal disaggregation techniques are used to obtain hourly precipitation series, following as a reference the work proposed by Förster et al. (2016) and Breinl and Di Baldassarre (2019). ...
Understanding the future patterns of precipitation behaviour in unique geographical areas, largely determined by their orography and local scale, can help lay the foundations for a new precipitation model for the design of the city’s main urban drainage infrastructures (intensity-duration-frequency curves, mathematical functions that relate precipitation intensity to duration and frequency of occurrence, hereafter IDF, for the short-, medium- and long-term future). This will definitely contribute to the improvement of the city’s resilience to the effects of climate change. In this paper, the projections of a subset of climate change models from both the sixth phase of the Coupled Model Intercomparison Project (CMIP6; with a total of 5 simulations) and Euro-CORDEX (for a set of 51 simulations) have been adjusted to the municipality of Alicante (in the southeast of Spain), using the Climadjust tool (climadjust.com). These projections contain different climatic variables. The rainfall variable has been used to derive a new framework of boundary conditions to help design more resilient infrastructure for torrential rainfall events and urban flooding. The projections corresponding to three climate change scenarios (CMIP6: SSP1-2.6, SSP2-4.5, SSP5-8.5; and Euro-CORDEX: RCP2.6, RCP4.5, RCP8.5) are considered with daily resolution and, by applying statistical techniques of temporal disaggregation (by means of a cascade model), hourly (and sub-hourly, reaching 30-min resolution) disaggregation. The results at hourly and 30-min resolutions are used to construct IDF curves of future climate, grouped into short-term (years 2015 to 2040), medium-term (years 2041 to 2070) and long-term (years 2071 to 2100) sub-scenarios. The selected future climate IDFs for an adverse climate change scenario (SSP2-4.5 and SSP5-8.5) show increases in rainfall intensities, higher the shorter the rainfall duration, for return periods greater than or equal to 25 years, whereas for return periods under 25 years the current IDFs can be representative of future scenarios. Current calculations and future projection of the torrentiality index for severe climate change scenarios, as well as the climate change factors, show an increase in the frequency and magnitude of the heaviest rainfall. This fact corroborates the hypotheses of greater general torrentiality in future rainfall in this specific area of the Spanish Mediterranean coast.
... For a day d, let P d denote the daily SPAZM precipitation at a pixel that we want to disaggregate. The method of fragments 490 (Wójcik and Buishand, 2003;Breinl and Di Baldassarre, 2019) consists in using the temporal structure of another precipitation data available at a finer scale and preserving the daily amounts. LetP h denote the hourly precipitation for this alternative source, where h = 1, . . . ...
Hydrological modelling of small mountainous catchments is particularly challenging because of the high spatio-temporal resolution required for the meteorological forcings. In-situ measurements of precipitation are typically scarce in these remote areas, particularly at high elevations. Precipitation reanalyses propose different alternative forcings for the simulation of streamflow using hydrological models. In this paper, we evaluate the performances of two hydrological models representing some of the key processes for small mountainous catchments, using different meteorological products with a fine spatial and temporal resolution. The evaluation is performed on 55 small catchments of the Northern French Alps. While the simulated streamflows are adequately reproduced for most of the configurations, these evaluations emphasize the added value of radar measurements, in particular for the reproduction of flood events. However, these better performances are only obtained because the hydrological models correct the underestimations of accumulated amounts (e.g. annual) from the radar data in high-elevation areas.
... A widely used method is the non-parametric method of fragments (MOF), where the disaggregation scheme for any target day is obtained from the high-resolution temporal (and spatial, if relevant) structure of a given analog day selected in the archive of observations (e.g. Mezghani and Hingray, 2009;Breinl and Di Baldassarre, 2019;Park and Chung, 2020;Acharya et al., 2022). By construction, MOF methods preserve the 35 sub-daily patterns of precipitation and the intermittency properties within each day. ...
Analytical Multiplicative Random Cascades (MRCs) are widely used for the temporal disaggregation of coarse-resolution precipitation time series. This class of models applies simple scaling laws to represent the dependence of the cascade generator on the temporal scale and the precipitation intensity. Although determinant, the dependence on the external precipitation pattern is usually disregarded. Our work presents a unified MRC modelling framework that allows the cascade generator to depend in a continuous way on temporal scale, precipitation intensity and a so-called precipitation asymmetry index. Different MRC configurations are compared for 81 locations in Switzerland with contrasted climates. The added value of the dependence of the MRC on the temporal scale appears to be unclear, unlike what was suggested in previous works. Introducing the precipitation asymmetry dependence in the model leads to a drastic improvement of model performance for all statistics related to precipitation temporal persistence (wet/dry transition probabilities, lag-n autocorrelation coefficients, lengths of dry/wet spells). Accounting for precipitation asymmetry seems to solve this important limitation of previous MRCs. The model configuration that only accounts for the dependence on precipitation intensity and asymmetry is highly parsimonious, with only five parameters, and provides adequate performances for all locations, seasons and temporal resolutions. The spatial coherency of the parameter estimates indicates a real potential for regionalisation and for further application to any location in Switzerland.
... Cowpertwait et al., 1996;Koutsoyiannis et al., 2003;Onof and Wang, 2020;Rodriguez-Iturbe et al., 1987, studied the cluster-based Poisson process for stochastic rainfall modeling. Wójcik and Buishand, 2003;Westra et al., 2012;Breinl et al., 2015;Breinl and Di Baldassarre, 2019, put forward another model based on the method of fragments. Olsson (1998) has modeled the scaling behavior of rainfall using a cascade process called microcanonical multiplicative random cascade (MMRC) model. ...
Temporal disaggregation of rainfall has been of particular focus because of the non-availability of higher-resolution rainfall data for a long-duration period. Fine temporal resolution rainfall is used in a multitude of hydrological applications. Researchers have proposed various disaggregation models to disaggregate coarse temporal resolution rainfall. In this paper, firstly, the microcanonical multiplicative random cascade (MMRC) model is applied for disaggregation from daily rainfall to a one-hour scale. The model is applied in four different rainfall stations for disaggregation having varying rainfall patterns and characteristics. It is observed that the MMRC model can generate statistically reliable rainfall time series; however, the extreme rainfall characteristics are not well conserved by the model for all the stations.
This paper describes a new model based on a random multiplicative cascade process where classification and parameter generation is done by k-means clustering such that it can better conserve extreme rainfall conditions and generate a reliable rainfall time series (MMRC-K). K-means clustering is a vector quantization method that divides the observations into a particular number of clusters based on the nearest mean called cluster centroid. The novel approach is tested with the same four Indian cities. The use of k-means clustering has made the classification and parameter generation of the model robust such that it can work with data sets of varying characteristics. It is found that MMRC-K provides improved conservation of extreme rainfall characteristics compared to the MMRC model for all four stations. The MMRC-K model reproduces the IDF curves of Delhi and Mumbai stations quite well; however, a little discrepancy was observed at higher resolution and larger return periods in Kolkata and Chennai stations. Extreme rainfall at finer resolution is used in various hydrological analyses and design problems like urban drainage design, stormwater management, etc. The overall superior conservation of the extreme rainfall characteristics in the model-generated rainfall time series by the MMRC-K model compared to the MMRC model supports the potential applicability of the model for temporal disaggregation.
... However, KNN uses the single criterion of daily precipitation depth to draw a sample from the historical/training space. Similarly other MOF methods use singular criteria like intensity, seasonality and similarity scores (Breinl and Di Baldassarre, 2019). This presents an opportunity for improvement in the methodological domain in terms of introducing multiple criteria for selection of fragments from the training space. ...
... The number of nearest neighbours is computed as k = ̅̅̅̅ ̅ n c √ (Breinl and Di Baldassarre, 2019;Lall and Sharma, 1996), where n c represents the sample size of the class members falling within the training data. For sampling between j neighbours, the following conditional probability distribution is used as described in Eq. (4) to (5) (Lall and Sharma, 1996;Pui et al., 2012): ...
This study addresses the issue of scant availability of sub-daily precipitation data by introducing a novel selection methodology named ‘Pattern Mapping’ (PM) within the existing Method of Fragments (MOF) framework for the disaggregation of daily precipitation. PM introduces multiple statistics based criterion in the selection of fragments thus enhancing accuracy of the selection process. The performance of deterministic and stochastic versions of PM-MOF is compared with three widely used disaggregation methods, namely K Nearest Neighbour based MOF (KNN-MOF), Bartlett-Lewis Rectangular Pulse model (using HYETOS software package) and Micro-Canonical Cascade (MCC) using reanalysis data at 14 global locations spanning various climatic zones. It is seen that the PM-MOF method has considerably lower percentage error in replicating the standard statistics (-50.2 to 50.3% for stochastic PM-MOF and -7.4 to 13.2% for deterministic PM-MOF) when compared to existing methods (KNN-MOF (-65.4 to 76.2%), HYETOS (-78.3 to 69.4%) and MCC (-63.1 to 72%)). The comparison of densities using skill score show that skill score of PM-MOF is 0.97 which is higher than other methods (0.94 for KNN-MOF, 0.83 for HYETOS and 0.85 for MCC). Control experiments designed around varying length of training data and stochastic/deterministic mode (of PM-MOF) ascertain the contribution of the novel methodological improvements in the superior performance of PM-MOF. The robustness of the methodology and geography independent performance of PM-MOF makes it a potent candidate for wider application in hydrological and climate studies.
... This disaggregation used the temporal structure of the respective variable observed, either for the same day if available at a nearby station or for an analogous day in the period with hourly continuous observations. The analogy was specified using surface weather for the region and applying constraints to preserve season and class of intensity following Breinl and Di Baldassarre (2019). The hydrological data encompass continuous discharge records at 65 stations (Table S2). ...
Estimates for rare to very rare floods are limited by the relatively short streamflow records available. Often, pragmatic conversion factors are used to quantify such events based on extrapolated observations, or simplifying assumptions are made about extreme precipitation and resulting flood peaks. Continuous simulation (CS) is an alternative approach that better links flood estimation with physical processes and avoids assumptions about antecedent conditions. However, long-term CS has hardly been implemented to estimate rare floods (i.e. return periods considerably larger than 100 years) at multiple sites in a large river basin to date. Here we explore the feasibility and reliability of the CS approach for 19 sites in the Aare River basin in Switzerland (area: 17 700 km2) with exceedingly long simulations in a hydrometeorological model chain. The chain starts with a multi-site stochastic weather generator used to generate 30 realizations of hourly precipitation and temperature scenarios of 10 000 years each. These realizations were then run through a bucket-type hydrological model for 80 sub-catchments and finally routed downstream with a simplified representation of main river channels, major lakes and relevant floodplains in a hydrologic routing system. Comprehensive evaluation over different temporal and spatial scales showed that the main features of the meteorological and hydrological observations are well represented and that meaningful information on low-probability floods can be inferred. Although uncertainties are still considerable, the explicit consideration of important processes of flood generation and routing (snow accumulation, snowmelt, soil moisture storage, bank overflow, lake and floodplain retention) is a substantial advantage. The approach allows for comprehensively exploring possible but unobserved spatial and temporal patterns of hydrometeorological behaviour. This is of particular value in a large river basin where the complex interaction of flows from individual tributaries and lake regulations are typically not well represented in the streamflow observations. The framework is also suitable for estimating more frequent floods, as often required in engineering and hazard mapping.
... Molnar and Burlando, 2005;Pohle et al., 2018;Müller and Haberlandt, 2018), method-of-fragments models (e.g. Breinl and Di Baldassarre, 2019), or alternating renewal models (e.g. Callau Poduje and Haberlandt, 2017) or as part of weather generators (Peleg et al., 2017). ...
Rainfall erosivity values are required for soil erosion prediction. To calculate the mean annual rainfall erosivity (R), long-term high-resolution observed rainfall data are required, which are often not available. To overcome the issue of limited data availability in space and time, four methods were employed and evaluated: direct regionalisation of R, regionalisation of 5 min rainfall, disaggregation of daily rainfall into 5 min time steps, and a regionalised stochastic rainfall model. The impact of station density is considered for each of the methods. The study is carried out using 159 recording and 150 non-recording (daily) rainfall stations in and around the federal state of Lower Saxony, Germany. In addition, the minimum record length necessary to adequately estimate R was investigated. Results show that the direct regionalisation of mean annual erosivity is best in terms of both relative bias and relative root mean square error (RMSE), followed by the regionalisation of the 5 min rainfall data, which yields better results than the rainfall generation models, namely an alternating renewal model (ARM) and a multiplicative cascade model. However, a key advantage of using regionalised rainfall models is the ability to generate time series that can be used for the estimation of the erosive event characteristics. This is not possible if regionalising only R. Using the stochastic ARM, it was assessed that more than 60 years of data are needed in most cases to reach a stable estimate of annual rainfall erosivity. Moreover, the temporal resolution of measuring devices was found to have a significant effect on R, with coarser temporal resolution leading to a higher relative bias.
... In general, the disaggregation approaches utilise sub-daily rainfall characteristics that are estimated from historical observations to generate sub-daily rainfall based on sub-daily rainfall statistics. Relevant disaggregation approaches include multiplicative cascade models (Lombardo et al., 2017;Haberlandt, 2018, 2015), multivariate techniques that preserve the required spatial and temporal dependencies (Koutsoyiannis, 2003;Müller and Haberlandt, 2018;Perica and Foufoula-Georgiou, 1996;Wasko et al., 2013;Wilks, 1998), and simple method-of-fragments (Breinl and Di Baldassarre, 2019;Pui et al., 2012;Westra et al., 2012). One of the core features of temporal disaggregation approaches is that they may use information from observed rainfall sources to preserve rainfall characteristics at coarser timestep (Lombardo et al., 2012;Papalexiou et al., 2018) and preserve selected time series characteristics such as autocorrelation Müller and Haberlandt, 2015), rainfall asymmetry at higher temporal resolutions (Müller et al., 2017), and rainfall intermittency (Gires et al., 2012;Schleiss and Smith, 2016). ...
... Considering that there are advanced (stochastic) disaggregation approaches which preserve such characteristics (e.g. Breinl and Di Baldassarre, 2019;Lombardo et al., 2017;Ma et al., 2020;Haberlandt, 2018, 2015;Seyyedi et al., 2014), if the resulting applications are sensitive to fine-scale rainfall characteristics, then it may not be appropriate to adopt the simple (deterministic) disaggregation approach presented in this study. ...
... This is also one of the strengths of the proposed disaggregation approach as it does not rely on additional parametric characterisation of spatial characteristics for instilling spatial consistency (e.g. Breinl and Di Baldassarre, 2019;Clark et al., 2004;Haberlandt, 2018, 2015;Wasko et al., 2013). However, the accuracy of the sub-daily characteristics is dependent on the quality of the reanalysis, and the nature of these associated uncertainties are described by Acharya et al (2020). ...
Accurate rainfall datasets with high temporal and spatial resolutions are crucial for most hydrological applications. One potentially valuable source of rainfall data that has consistent spatial and temporal resolutions are atmospheric reanalysis products. However, while such data sets can provide a physically consistent representation of rainfall over large spatial and temporal extents, they are generally less accurate than observed datasets at daily scales. In contrast, while the gauge measurements are accurate source of rainfall data, sub-daily observations are spatially sparse and are of shorter length than daily observations. While the temporal resolution of daily observations can be enhanced using temporal disaggregation methods, they are often applied stochastically with a focus on capturing the fine-scale statistical properties rather than generating a best estimate time series useful for hindcasting purposes. The increasing availablity of high resolution regional reanalysis products prompts the question whether they can be used to temporally disaggregate daily observations to derive high-resolution estimates of sub-daily rainfalls suitable for hydrologic applications. This study investigates the efficacy of a simple disaggregation approach to temporally disaggregate daily rainfalls to hourly values using a regional reanalysis at moderate spatial resolutions. The approach is tested on attributes relevant to a wide range of hydrological applications. The selected performance metrics include the distribution and frequency of various sub-daily rainfall accumulations, statistics characterising the sequencing and central tendency of sub-daily rainfalls, and the efficacy of areal estimates of sub-daily rainfalls for simulating catchment streamflows. Categorical evaluation shows that the disaggregated rainfalls reduce the frequency of false alarms and improves the probability of detection compared to the use of raw reanalysis estimates. However, a mixed performance in capturing fine-scale statistical characteristics suggests that the disaggregation approach is less robust for applications that rely solely on high-resolution rainfall characteristics. In hydrological evaluation, when compared to estimates based on raw reanalysis or uniformly disaggregated daily observations, the disaggregated catchment rainfalls improve the simulation of the magnitude and timing of peak flows, and the accuracy of derived flood frequency estimates. The proposed disaggregation method is easily applied to any high-resolution dataset and has the potential to be used in hydrological applications that rely heavily on sub-daily characterisation, with a varying performance across the target applications.
