Statistics for Spatial Data.

Advances in numerical weather prediction represent a quiet revolution because they have resulted from a steady accumulation of scientific knowledge and technological advances over many years that, with only a few exceptions, have not been associated with the aura of fundamental physics breakthroughs. Nonetheless, the impact of numerical weather prediction is among the greatest of any area of physical science. As a computational problem, global weather prediction is comparable to the simulation of the human brain and of the evolution of the early Universe, and it is performed every day at major operational centres across the world.

The quiet revolution of numerical weather prediction

Evidence that extreme rainfall intensity is increasing at the global scale has strengthened considerably in recent years Research now indicates that the greatest increases are likely to occur in short-duration storms lasting less than a day, potentially leading to an increase in the magnitude and frequency of flash floods This review examines the evidence for subdaily extreme rainfall intensification due to anthropogenic climate change and describes our current physical understanding of the association between subdaily extreme rainfall intensity and atmospheric temperature We also examine the nature, quality, and quantity of information needed to allow society to adapt successfully to predicted future changes, and discuss the roles of observational and modeling studies in helping us to better understand the physical processes that can influence subdaily extreme rainfall characteristics We conclude by describing the types of research required to produce a more thorough understanding of the relationships between local-scale thermodynamic effects, large-scale atmospheric circulation, and subdaily extreme rainfall intensity

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014RG000464

Future changes to the intensity and frequency of short‐duration extreme rainfall

The Prediction in Ungauged Basins (PUB) initiative of the International Association of Hydrological Sciences (IAHS), launched in 2003 and concluded by the PUB Symposium 2012 held in Delft (23–25 October 2012), set out to shift the scientific culture of hydrology towards improved scientific understanding of hydrological processes, as well as associated uncertainties and the development of models with increasing realism and predictive power. This paper reviews the work that has been done under the six science themes of the PUB Decade and outlines the challenges ahead for the hydrological sciences community.Editor D. KoutsoyiannisCitation Hrachowitz, M., Savenije, H.H.G., Bloschl, G., McDonnell, J.J., Sivapalan, M., Pomeroy, J.W., Arheimer, B., Blume, T., Clark, M.P., Ehret, U., Fenicia, F., Freer, J.E., Gelfan, A., Gupta, H.V., Hughes, D.A., Hut, R.W., Montanari, A., Pande, S., Tetzlaff, D., Troch, P.A., Uhlenbrook, S., Wagener, T., Winsemius, H.C., Woods, R.A., Zehe, E., and Cudennec, C., 2013. A d...

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A decade of Predictions in Ungauged Basins (PUB)—a review

Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art

An ensemble-based probabilistic precipitation forecasting scheme has been developed that blends an extrapolation nowcast with a downscaled NWP forecast, known as STEPS: Short-Term Ensemble Prediction System. The uncertainties in the motion and evolution of radar-inferred precipitation fields are quantified, and the uncertainty in the evolution of the precipitation pattern is shown to be the more important. The use of ensembles allows the scheme to be used for applications that require forecasts of the probability density function of areal and temporal averages of precipitation, such as fluvial flood forecasting—a capability that has not been provided by previous probabilistic precipitation nowcast schemes. The output from a NWP forecast model is downscaled so that the small scales not represented accurately by the model are injected into the forecast using stochastic noise. This allows the scheme to better represent the distribution of precipitation rate at spatial scales finer than those adequately resolved by operational NWP. The performance of the scheme has been assessed over the month of March 2003. Performance evaluation statistics show that the scheme possesses predictive skill at lead times in excess of six hours. © Crown copyright, 2006.

STEPS: A probabilistic precipitation forecasting scheme which merges an extrapolation nowcast with downscaled NWP

Quantitative nowcasts of rainfall are frequently based on the advection of rain fields observed by weather radar. Spectral Prognosis (S-PROG) is an advection-based nowcasting system that uses the observations that rain fields commonly exhibit both spatial and dynamic scaling properties, that is, the lifetime of a feature in the field is dependent on the scale of the feature (large features evolve more slowly than small features), and that features at all scales between the outer and inner observed scales are present in the field. The logarithm of the radar reflectivity field is disaggregated into a set or cascade of fields, in which each field in the set (or level in the cascade) represents the features of the original field over a limited range of scales. The Lagrangian temporal evolution of each level in the cascade is modeled using a simple autoregressive (lag 2) model, which automatically causes the forecast field to become smooth as the structures at the various scales evolve through their life cycles, or can be used to generate conditional simulations if the noise term is included. This paper describes the model and presents preliminary results.

A Dynamic and Spatial Scaling Approach to Advection Forecasting

The connection among different types of exponents characterizing multiscaling properties of rainfall and a criterion for stationarity of random fields are discussed, and a new phenomenological model for rainfall time series simulation is proposed. The bounded random cascade model presented here is a generalization of the well-known α model with the multiplicative weights of the generator converging to unity as the cascade proceeds to smaller scales. This allows one to directly simulate a multiscaling random field with an energy spectrum exponent, β>1, which is typical for rainfall time series data but which cannot be produced by a standard α model. A procedure is proposed for estimating the cascade parameters of this new bounded α model from observed data. Parameters are estimated from two data sets with different degrees of intermittency and different spectral exponents. The bounded α model simulations using these parameters produced realistic rainfall time series with spectral exponents similar to their observed counterparts.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97WR02006

Multiscaling properties of rainfall and bounded random cascades

The simple scaling hypothesis is applied to the intensity-duration-frequency (IDF) description of rainfall. It is shown that the cumulative distribution function for the annual maximum series of mean rainfall intensity has a simple scaling property over the range 30 min to 24 hours and in some instances to 48 hours. This behavior is demonstrated through an examination of the scaling properties of the moments and the scaling of the parameters of an extreme value distribution fitted to the data. A simple analytical formula for the IDF relationship is proposed, which embodies the scaling behavior. Once the scaling parameter has been obtained for a gauge or set of gauges in a region, this formula enables the calculation of rainfall amounts, of a chosen return period and duration shorter than a day, directly from the information obtained from the analysis of daily data.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1998WR900012

Alan Seed

Papers

STEPS: A probabilistic precipitation forecasting scheme which merges an extrapolation nowcast with downscaled NWP

A Dynamic and Spatial Scaling Approach to Advection Forecasting

Multiscaling properties of rainfall and bounded random cascades

A simple scaling model for extreme rainfall

Development of a precipitation nowcasting algorithm based upon optical flow techniques