Carlo De Michele | Politecnico di Milano (original) (raw)

Papers by Carlo De Michele

Climate change is a living topic when dealing with modern natural sciences. The increase in the a... more Climate change is a living topic when dealing with modern natural sciences. The increase in the average air temperature, as measured in the last decades, is considered as the most relevant effect of climate change on the Earth system. Since the air temperature has a key role in determining the partitioning between liquid and solid precipitation events at a site, important changes in rainfall dynamics are expected, especially in mountainous areas. Thus, an important issue for modern hydrology is to determine how climate change would affect the liquid-solid partitioning of precipitation and its statistical properties. The main aim here is to determine, via statistical analysis and goodness-of-fit tests, whether the duration of precipitation events under the different forms (namely solid, liquid and mixed) may be characterized by the same probability distribution. Similar issue is tested for the volume of precipitation. For this aim, our study pays attention to hourly data collected along an altitude gradient identified through six automatic weather stations in Trentino region, northeast Italy. To distinguish the different types of events from observed heated pluviometers' data, a partitioning procedure has been used and validated, through some disdrometer data. Sample data of duration and volume, relatively to solid, liquid and mixed events, are extracted, and univariate and bivariate statistics are calculated. Then, the two-sample Kolmogorov-Smirnov test is used to test if the data distinguished by different types of precipitation can be considered extracted from the same distribution. The results showed that in most cases, durations, as well as volumes of the different types of events, cannot be considered equally distributed. This consideration is particularly clear at high elevations.

PLoS ONE, 2014

Moist savannas and tropical forests share the same climatic conditions and occur side by side. Ex... more Moist savannas and tropical forests share the same climatic conditions and occur side by side. Experimental evidences show that the tree cover of these ecosystems exhibits a bimodal frequency distribution. This is considered as a proof of savannaforest bistability, predicted by dynamic vegetation models based on non-linear differential equations. Here, we propose a change of perspective about the bimodality of tree cover distribution. We show, using a simple matrix model of tree dynamics, how the bimodality of tree cover can emerge from the switching between two linear dynamics of trees, one in presence and one in absence of fire, with a feedback between fire and trees. As consequence, we find that the transitions between moist savannas and tropical forests, if sharp, are not necessarily catastrophic.

Hydrology and Earth System Sciences, 2011

Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous... more Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according 5 to different criteria: these may use either a nearest neighbor or a nearest cluster approach, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.

Hydrological Processes, 2009

Snow accumulation and ablation rule the temporal dynamics of water availability in mountain areas... more Snow accumulation and ablation rule the temporal dynamics of water availability in mountain areas and cold regions. In these environments, the evaluation of the snow water amount is a key issue. The spatial distribution of snow water equivalent (SWE) over a mountain basin at the end of the snow accumulation season is estimated using a minimal statistical model (SWE-SEM). This uses systematic observations such as ground measurements collected at snow gauges and snow-covered area (SCA) data retrieved by remote sensors, here MODIS. Firstly, SWE-SEM calculates local SWE estimates at snow gauges, then the spatial distribution of SWE over a certain area using an interpolation method; linear regressions of the first two order moments of SWE with altitude. The interpolation has been made by both confining and unconfining the spatial domain by SCA. SWE-SEM is applied to the Mallero basin (northern Italy) for calculating the snow water equivalent at the end of the winter season for 6 years (2001–2007). For 2007, SWE-SEM estimates are validated through fieldwork measurements collected during an ‘ad hoc’ campaign on March 31, 2007. Snow-surveyed measurements are used to check SCA, snow density and SWE estimates. Copyright © 2009 John Wiley & Sons, Ltd.

Hydrology and Earth System Sciences Discussions, 2011

Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo... more Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo and De Michele, 2011), to investigate the variability of instantaneous renormalized spectra of drop diameter in presence of orographic precipitation. Disdrometer data, available at Bodega Bay and Cazadero, California, are analyzed either as whole, or as divided (using the bright band echo) in precipitation intervals weakly and strongly influenced by orography, and compared to results obtained at Darwin, Australia. We find that also at Bodega Bay and Cazadero exists a most common distribution for the instantaneous renormalized spectra. The skewness values associated with the most common distributions are larger than those found at Darwin. No appreciable differences are found in the skewness distributions of precipitation weakly and strongly influenced by orography. However the renormalized drop diameter spectra of precipitation with strong orographic component have fatter right tail than precipitation with a weaker orographic component. The differences between orographic and non-orographic precipitation are investigated within the parametric space represented by number of drops, mean value and standard deviation of drop diameter. A filter is developed which is able to identify 1 min time intervals during which precipitation is mostly of orographic origin.

Physics Today, 2011

The discrete charm of rain. [Physics Today 64, 68 (2011)]. Massimiliano Ignaccolo,Carlo De Michel... more The discrete charm of rain. [Physics Today 64, 68 (2011)]. Massimiliano Ignaccolo,Carlo De Michele. Keywords. Hydrological modeling; general theory. Precipitation (hydrological). Precipitation. Weather analysis and prediction.

Advances in Water Resources, 2010

In this manuscript, we show that 1) the rain event definition resting on the occurrence of a mini... more In this manuscript, we show that 1) the rain event definition resting on the occurrence of a minimum rainless period and the one resting on a sequence of consecutive wet intervals are statistically equivalent. 2) It is possible to obtain a point based Eulerian event definition using the ...

Journal of Hydrometeorology, 2009

This study looks for statistically invariant properties of the sequences of inter-drop time inter... more This study looks for statistically invariant properties of the sequences of inter-drop time intervals and drop diameters. The authors provide evidence that these invariant properties have the following characteristics: 1) large inter-drop time intervals (*10 s) separate drops of small diameter (&0.6 mm); 2) the rainfall phenomenon has two phases: a quiescent phase, whose contribution to the total cumulated flux is virtually null, and an active, nonquiescent, phase that is responsible for the bulk of the precipitated volume; 3) the probability density function of inter-drop time intervals has a power-law-scaling regime in the range of ;1 min and ;3 h); and 4) once the moving average and moving standard deviation are removed from the sequence of drop diameters, an invariant shape emerges for the probability density function of drop diameters during active phases.

A long standing issue in Hydrology is the arbitrariness of the rain "event" definition. In this m... more A long standing issue in Hydrology is the arbitrariness of the rain "event" definition. In this manuscript, we show that 1) the event definition resting on the occurrence of a minimum rainless period and the one resting a sequence of consecutive wet intervals are statistically equivalent. 2) In the case of stratiform rain, a non arbitrary definition of rain event is possible. The dynamical properties of stratiform rain indicate the range [1.5,4] h as the proper one for the choice of a minimum rainless period for Chilbolton, UK. 3) The intra event dynamical variability is "described" by an alternate sequence of quiescent and active phases.

This study is aimed at demonstrating the feasibility of the MODIS Land Surface Temperature (LST) ... more This study is aimed at demonstrating the feasibility of the MODIS Land Surface Temperature (LST) product as a source for calculating spatially distributed daily mean air temperature to be used as input for hydrological or environmental models. The test area is located in the Italian Alpine area. The proposed procedure solves, by empirical approaches, the problem of relating LST to the Air Temperature (T air ) and instantaneous T air values to daily mean values, exploiting ground data weather station measurements as a reference. The relationship between LST and T air is determined by correlation analysis and equation generalisation for spatial distribution. The extrapolation of daily mean values of T air from instantaneous values is addressed again by correlation analyses taking into account the altitude variability and exploiting historical series. Validation was accomplished by accuracy assessment procedures both punctual and spatially distributed, the latter performed by comparison with the Inverse Distance Weighting (IDW) interpolation method.

Water Resources Research, 2004

1] In this paper we provide a general theoretical framework exploiting copulas for studying the r... more 1] In this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events; in particular, we consider events depending upon the joint behavior of two nonindependent random variables, an approach which can easily be generalized to the multivariate case. We show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods, both in the unconditional and in the conditional case. In addition, we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub-, super-, and critical events as well as those of primary and secondary return periods. An illustration of the techniques proposed is provided by analyzing some case studies already examined in literature.

The self-similarity conjecture can provide an assessment of regionalization procedures for flood ... more The self-similarity conjecture can provide an assessment of regionalization procedures for flood frequency analysis if the scaling properties of flood flows as parameterised by drainage area are considered. The question whether simple scaling can be used to discriminate among different flood probabilities in relatively small regions with high variability of climate and geomorphological features is investigated. Detailed simulations for a small basin in Thyrrhenian Liguria (North-West Italy) show that self-similarity or simple scaling properly represent the spatial variability of flood probabilities. The scaling properties of annual flood series for North-West Italy are also investigated. Although flood statistics display multiscaling properties when considering North-West Italy as an individual homogeneous region, one can classify geographically consistent regions in this area where self-similarity cannot be rejected. Accordingly, the index flood procedure can be properly applied to these regions in order to estimate flood probabilities at ungauged catchments, and the scaling exponent of flood probabilities can be interpreted as the signature of complex interactions between climate and hydrology producing extreme flows in rivers of a region. This conjecture is substantiated by the common scaling exponent of flood probabilities resulting from both basin simulations and frequency analysis of annual series for the region including this basin.

Geophysical Research Letters, 2004

Hydrology and Earth System Sciences, 2003

Index flood estimation for regional flood frequency analysis needs to be based on the information... more Index flood estimation for regional flood frequency analysis needs to be based on the information available. The most appropriate method depends on the specific application and its choice requires a problem-oriented analysis. This paper presents a simple theoretical framework to deal with index flood estimation for a specific river site. The methodological approaches available for the purpose are reviewed. For each, the information required is specified and the reliability of the estimate, particularly desirable in risk analysis and management, is discussed. Where flood observations are lacking, indirect estimation must be undertaken using scenarios including those commonly met in hydrological practice; generally, these depend on the amount and type of information available. For each scenario, the methodologies are outlined, in order of the expected degree of complexity. After a guided analysis, an investigator can adopt the method providing the best tradeoff between effort in collecting and handling data and the resultant reliability which can be expected.

Water Resources Research, 2001

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is wi... more We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.

Journal of Hydrologic Engineering, 2005

... for the design of dam spillways. Acknowledgments. The research was partially supported by MUR... more ... for the design of dam spillways. Acknowledgments. The research was partially supported by MURST via the project “Hydrological Safety of Impounded Rivers.” The support of “Progetto Giovani Ricercatori” is also acknowledged. Estimated Values of Two Measures of Association ...

Journal of Hydrology, 2002

In this paper we present an analytical formulation of the derived distribution of peak¯ood and ma... more In this paper we present an analytical formulation of the derived distribution of peak¯ood and maximum annual peak¯ood, starting from a simpli®ed description of rainfall and surface runoff processes, and we show how such a distribution is useful in practical applications. The assumptions on rainfall dynamics include the hypotheses that the maximum storm depth has a Generalized Pareto distribution, and that the temporal variability of rainfall depth in a storm can be described via power±law relationships. The SCS-CN model is used to describe the soil response, and a lumped model is adopted to transform the rainfall excess into peak¯ood; in particular, we analyse the in¯uence of antecedent soil moisture condition on the¯ood frequency distribution. We then calculate the analytical expressions of the derived distributions of peak¯ood and maximum annual peak ood. Finally, practical case studies are presented and discussed. q

Water Resources Research, 2001

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is wi... more We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.

A method for index flood estimation is presented, using jointly the statistical and the derived d... more A method for index flood estimation is presented, using jointly the statistical and the derived distribution approaches, in order to combine the main features of each one. The statistical approach is used to represent the process of occurrence of peak flows, whereas the derived distribution one is adopted to relate flood frequency with climatic, géomorphologie and pédologie factors in a parsimonious representation. The proposed methodology, relating index flood to the parameters of the GEV regional growth curve and to a few parameters characterizing the relevant géomorphologie and climatic properties of the single catchment, allows the estimation of the index flood for ungauged sites. Its application to a large region of northern Italy, including Po River basin and Thyrrhenian Liguria, is presented.

Journal of Hydrologic Engineering, 2003

Climate change is a living topic when dealing with modern natural sciences. The increase in the a... more Climate change is a living topic when dealing with modern natural sciences. The increase in the average air temperature, as measured in the last decades, is considered as the most relevant effect of climate change on the Earth system. Since the air temperature has a key role in determining the partitioning between liquid and solid precipitation events at a site, important changes in rainfall dynamics are expected, especially in mountainous areas. Thus, an important issue for modern hydrology is to determine how climate change would affect the liquid-solid partitioning of precipitation and its statistical properties. The main aim here is to determine, via statistical analysis and goodness-of-fit tests, whether the duration of precipitation events under the different forms (namely solid, liquid and mixed) may be characterized by the same probability distribution. Similar issue is tested for the volume of precipitation. For this aim, our study pays attention to hourly data collected along an altitude gradient identified through six automatic weather stations in Trentino region, northeast Italy. To distinguish the different types of events from observed heated pluviometers' data, a partitioning procedure has been used and validated, through some disdrometer data. Sample data of duration and volume, relatively to solid, liquid and mixed events, are extracted, and univariate and bivariate statistics are calculated. Then, the two-sample Kolmogorov-Smirnov test is used to test if the data distinguished by different types of precipitation can be considered extracted from the same distribution. The results showed that in most cases, durations, as well as volumes of the different types of events, cannot be considered equally distributed. This consideration is particularly clear at high elevations.

PLoS ONE, 2014

Moist savannas and tropical forests share the same climatic conditions and occur side by side. Ex... more Moist savannas and tropical forests share the same climatic conditions and occur side by side. Experimental evidences show that the tree cover of these ecosystems exhibits a bimodal frequency distribution. This is considered as a proof of savannaforest bistability, predicted by dynamic vegetation models based on non-linear differential equations. Here, we propose a change of perspective about the bimodality of tree cover distribution. We show, using a simple matrix model of tree dynamics, how the bimodality of tree cover can emerge from the switching between two linear dynamics of trees, one in presence and one in absence of fire, with a feedback between fire and trees. As consequence, we find that the transitions between moist savannas and tropical forests, if sharp, are not necessarily catastrophic.

Hydrology and Earth System Sciences, 2011

Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous... more Multivariate Extreme Value models are a fundamental tool in order to assess potentially dangerous events. Exploiting recent theoretical developments in the theory of Copulas, new multiparameter models can be easily constructed. In this paper we suggest several strategies in order to estimate the parameters of the selected copula, according 5 to different criteria: these may use either a nearest neighbor or a nearest cluster approach, or exploit all the pair-wise relationships between the available gauge stations. An application to flood data is also illustrated and discussed.

Hydrological Processes, 2009

Snow accumulation and ablation rule the temporal dynamics of water availability in mountain areas... more Snow accumulation and ablation rule the temporal dynamics of water availability in mountain areas and cold regions. In these environments, the evaluation of the snow water amount is a key issue. The spatial distribution of snow water equivalent (SWE) over a mountain basin at the end of the snow accumulation season is estimated using a minimal statistical model (SWE-SEM). This uses systematic observations such as ground measurements collected at snow gauges and snow-covered area (SCA) data retrieved by remote sensors, here MODIS. Firstly, SWE-SEM calculates local SWE estimates at snow gauges, then the spatial distribution of SWE over a certain area using an interpolation method; linear regressions of the first two order moments of SWE with altitude. The interpolation has been made by both confining and unconfining the spatial domain by SCA. SWE-SEM is applied to the Mallero basin (northern Italy) for calculating the snow water equivalent at the end of the winter season for 6 years (2001–2007). For 2007, SWE-SEM estimates are validated through fieldwork measurements collected during an ‘ad hoc’ campaign on March 31, 2007. Snow-surveyed measurements are used to check SCA, snow density and SWE estimates. Copyright © 2009 John Wiley & Sons, Ltd.

Hydrology and Earth System Sciences Discussions, 2011

Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo... more Here we use the skewness parameter, and the procedure developed in the companion paper (Ignaccolo and De Michele, 2011), to investigate the variability of instantaneous renormalized spectra of drop diameter in presence of orographic precipitation. Disdrometer data, available at Bodega Bay and Cazadero, California, are analyzed either as whole, or as divided (using the bright band echo) in precipitation intervals weakly and strongly influenced by orography, and compared to results obtained at Darwin, Australia. We find that also at Bodega Bay and Cazadero exists a most common distribution for the instantaneous renormalized spectra. The skewness values associated with the most common distributions are larger than those found at Darwin. No appreciable differences are found in the skewness distributions of precipitation weakly and strongly influenced by orography. However the renormalized drop diameter spectra of precipitation with strong orographic component have fatter right tail than precipitation with a weaker orographic component. The differences between orographic and non-orographic precipitation are investigated within the parametric space represented by number of drops, mean value and standard deviation of drop diameter. A filter is developed which is able to identify 1 min time intervals during which precipitation is mostly of orographic origin.

Physics Today, 2011

The discrete charm of rain. [Physics Today 64, 68 (2011)]. Massimiliano Ignaccolo,Carlo De Michel... more The discrete charm of rain. [Physics Today 64, 68 (2011)]. Massimiliano Ignaccolo,Carlo De Michele. Keywords. Hydrological modeling; general theory. Precipitation (hydrological). Precipitation. Weather analysis and prediction.

Advances in Water Resources, 2010

In this manuscript, we show that 1) the rain event definition resting on the occurrence of a mini... more In this manuscript, we show that 1) the rain event definition resting on the occurrence of a minimum rainless period and the one resting on a sequence of consecutive wet intervals are statistically equivalent. 2) It is possible to obtain a point based Eulerian event definition using the ...

Journal of Hydrometeorology, 2009

This study looks for statistically invariant properties of the sequences of inter-drop time inter... more This study looks for statistically invariant properties of the sequences of inter-drop time intervals and drop diameters. The authors provide evidence that these invariant properties have the following characteristics: 1) large inter-drop time intervals (*10 s) separate drops of small diameter (&0.6 mm); 2) the rainfall phenomenon has two phases: a quiescent phase, whose contribution to the total cumulated flux is virtually null, and an active, nonquiescent, phase that is responsible for the bulk of the precipitated volume; 3) the probability density function of inter-drop time intervals has a power-law-scaling regime in the range of ;1 min and ;3 h); and 4) once the moving average and moving standard deviation are removed from the sequence of drop diameters, an invariant shape emerges for the probability density function of drop diameters during active phases.

A long standing issue in Hydrology is the arbitrariness of the rain "event" definition. In this m... more A long standing issue in Hydrology is the arbitrariness of the rain "event" definition. In this manuscript, we show that 1) the event definition resting on the occurrence of a minimum rainless period and the one resting a sequence of consecutive wet intervals are statistically equivalent. 2) In the case of stratiform rain, a non arbitrary definition of rain event is possible. The dynamical properties of stratiform rain indicate the range [1.5,4] h as the proper one for the choice of a minimum rainless period for Chilbolton, UK. 3) The intra event dynamical variability is "described" by an alternate sequence of quiescent and active phases.

This study is aimed at demonstrating the feasibility of the MODIS Land Surface Temperature (LST) ... more This study is aimed at demonstrating the feasibility of the MODIS Land Surface Temperature (LST) product as a source for calculating spatially distributed daily mean air temperature to be used as input for hydrological or environmental models. The test area is located in the Italian Alpine area. The proposed procedure solves, by empirical approaches, the problem of relating LST to the Air Temperature (T air ) and instantaneous T air values to daily mean values, exploiting ground data weather station measurements as a reference. The relationship between LST and T air is determined by correlation analysis and equation generalisation for spatial distribution. The extrapolation of daily mean values of T air from instantaneous values is addressed again by correlation analyses taking into account the altitude variability and exploiting historical series. Validation was accomplished by accuracy assessment procedures both punctual and spatially distributed, the latter performed by comparison with the Inverse Distance Weighting (IDW) interpolation method.

Water Resources Research, 2004

1] In this paper we provide a general theoretical framework exploiting copulas for studying the r... more 1] In this paper we provide a general theoretical framework exploiting copulas for studying the return periods of hydrological events; in particular, we consider events depending upon the joint behavior of two nonindependent random variables, an approach which can easily be generalized to the multivariate case. We show that using copulas may greatly simplify the calculations and may even yield analytical expressions for the isolines of the return periods, both in the unconditional and in the conditional case. In addition, we show how a new probability distribution may be associated with the return period of specific events and introduce the definitions of sub-, super-, and critical events as well as those of primary and secondary return periods. An illustration of the techniques proposed is provided by analyzing some case studies already examined in literature.

The self-similarity conjecture can provide an assessment of regionalization procedures for flood ... more The self-similarity conjecture can provide an assessment of regionalization procedures for flood frequency analysis if the scaling properties of flood flows as parameterised by drainage area are considered. The question whether simple scaling can be used to discriminate among different flood probabilities in relatively small regions with high variability of climate and geomorphological features is investigated. Detailed simulations for a small basin in Thyrrhenian Liguria (North-West Italy) show that self-similarity or simple scaling properly represent the spatial variability of flood probabilities. The scaling properties of annual flood series for North-West Italy are also investigated. Although flood statistics display multiscaling properties when considering North-West Italy as an individual homogeneous region, one can classify geographically consistent regions in this area where self-similarity cannot be rejected. Accordingly, the index flood procedure can be properly applied to these regions in order to estimate flood probabilities at ungauged catchments, and the scaling exponent of flood probabilities can be interpreted as the signature of complex interactions between climate and hydrology producing extreme flows in rivers of a region. This conjecture is substantiated by the common scaling exponent of flood probabilities resulting from both basin simulations and frequency analysis of annual series for the region including this basin.

Geophysical Research Letters, 2004

Hydrology and Earth System Sciences, 2003

Index flood estimation for regional flood frequency analysis needs to be based on the information... more Index flood estimation for regional flood frequency analysis needs to be based on the information available. The most appropriate method depends on the specific application and its choice requires a problem-oriented analysis. This paper presents a simple theoretical framework to deal with index flood estimation for a specific river site. The methodological approaches available for the purpose are reviewed. For each, the information required is specified and the reliability of the estimate, particularly desirable in risk analysis and management, is discussed. Where flood observations are lacking, indirect estimation must be undertaken using scenarios including those commonly met in hydrological practice; generally, these depend on the amount and type of information available. For each scenario, the methodologies are outlined, in order of the expected degree of complexity. After a guided analysis, an investigator can adopt the method providing the best tradeoff between effort in collecting and handling data and the resultant reliability which can be expected.

Water Resources Research, 2001

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is wi... more We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.

Journal of Hydrologic Engineering, 2005

... for the design of dam spillways. Acknowledgments. The research was partially supported by MUR... more ... for the design of dam spillways. Acknowledgments. The research was partially supported by MURST via the project “Hydrological Safety of Impounded Rivers.” The support of “Progetto Giovani Ricercatori” is also acknowledged. Estimated Values of Two Measures of Association ...

Journal of Hydrology, 2002

In this paper we present an analytical formulation of the derived distribution of peak¯ood and ma... more In this paper we present an analytical formulation of the derived distribution of peak¯ood and maximum annual peak¯ood, starting from a simpli®ed description of rainfall and surface runoff processes, and we show how such a distribution is useful in practical applications. The assumptions on rainfall dynamics include the hypotheses that the maximum storm depth has a Generalized Pareto distribution, and that the temporal variability of rainfall depth in a storm can be described via power±law relationships. The SCS-CN model is used to describe the soil response, and a lumped model is adopted to transform the rainfall excess into peak¯ood; in particular, we analyse the in¯uence of antecedent soil moisture condition on the¯ood frequency distribution. We then calculate the analytical expressions of the derived distributions of peak¯ood and maximum annual peak ood. Finally, practical case studies are presented and discussed. q

Water Resources Research, 2001

We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is wi... more We present a method of modeling the areal reduction factor (ARF) of storm rainfall. The ARF is widely used in reducing point rainfall to obtain areal average values for the same duration, probability of exceedance, and specified area. The concepts of scaling and multiscaling, developed in recent years, provide a powerful framework for studying spatial and temporal variability of hydrological processes. It is our view that ARF must reflect the scaling properties of rainfall in space and time. We develop a simple statistical approach to the ARF of extreme storm rainfall based on the scaling properties of the underlying process in space and time. We derive the scaling relations of mean rainfall intensity over an area A and for a duration T using the concepts of dynamic scaling and statistical self-affinity. A new physically based formula for the ARF is then obtained. Applications are made to observations from the metropolitan area of Milan, Italy, and to data in the United Kingdom, as given in the Natural Environmental Research Council Flood Studies Report. These studies indicate that storm rates in space and time are scaling for extreme events, and hence this concept is shown to provide a useful practical approach to the evaluation of design storms for specified areas.

A method for index flood estimation is presented, using jointly the statistical and the derived d... more A method for index flood estimation is presented, using jointly the statistical and the derived distribution approaches, in order to combine the main features of each one. The statistical approach is used to represent the process of occurrence of peak flows, whereas the derived distribution one is adopted to relate flood frequency with climatic, géomorphologie and pédologie factors in a parsimonious representation. The proposed methodology, relating index flood to the parameters of the GEV regional growth curve and to a few parameters characterizing the relevant géomorphologie and climatic properties of the single catchment, allows the estimation of the index flood for ungauged sites. Its application to a large region of northern Italy, including Po River basin and Thyrrhenian Liguria, is presented.

Journal of Hydrologic Engineering, 2003