Oscar J. Mesa

Multiscaling theory of flood peaks: Regional quantile analysis

We study the spatial random field of peak flows indexed by a channel network. Invariance of the probability distributions of peak flows under translation on this indexing set defines statistical homogeneity in a network. It implies that floods can be indexed by the network magnitude, or equivalently the drainage area, which serves as a scale parameter. This definition generalizes to homogeneity of flows in a geographical region containing several networks which are not necessarily the subnetworks of a single network. The widely used quantile regression method of the United States Geological Survey (USGS) provides one simple criterion to approximately designate homogeneous geographic regions. It is argued that the redefinition of homogeneity via the constancy of the coefficient of variation (CV) of floods implied by the index flood assumption is ad hoc. Invariance of the probability distributions of peak flows under scale change is used to develop the simple scaling and the multiscaling theories of regional floods in terms of their quantiles. The simple scaling theory predicts a constant CV and log-log linearity between flood quantiles and drainage areas such that the slopes in these equations do not change with the probability of exceedance. Multiscaling theory of floods is developed to exhibit differences in floods between small and large basins. This theory shows that the CV for small basins increases, and for large basins it decreases, as area increases. Moreover, the quantiles do not obey log-log linearity with respect to drainage areas. However, for large basins an approximate log-log linearity between quantiles and drainage areas is shown to hold. The slopes in these equations decrease as p decreases; i.e., larger floods have smaller slopes than smaller floods. This approximation provides a theoretical interpretation of the results of the empirical quantile regression method in homogeneous regions where simple scaling or the index flood assumption does not hold. Recent results on physical interpretations of the scaling theories are also summarized here. A simple nonlinear method is developed to estimate the parameters in the multiscaling theory. This method and other features of the theory are illustrated using flood data from central Appalachia in the United States.

Feedbacks between Hydrological Processes in Tropical South America and Large-Scale Ocean–Atmospheric Phenomena

Abstract The hydroclimatology of tropical South America is strongly coupled to low-frequency large-scale oceanicand atmospheric phenomena occurring over the Pacific and the Atlantic Oceans. In particular, El Nino–SouthernOscillation (ENSO) affects climatic and hydrologic conditions on timescales ranging from seasons to decades.With some regional differences in timing and amplitude, tropical South America exhibits negative rainfall andstreamflow anomalies in association with the low–warm phase of the Southern Oscillation (El Nino), and positiveanomalies with the high–cold phase. Such dependence is illustrated in the hydroclimatology of Colombia throughseveral empirical analyses: correlation, empirical orthogonal functions, principal component, and spectral analysis, and discussion of the major physical mechanisms. Observations show that ENSO’s effect on river dischargesoccurs progressively later for rivers toward the east in Colombia and northern South America. Also, the impactsof La Nina are more pronounc...

On the existence of Lloró (the rainiest locality on Earth): Enhanced ocean‐land‐atmosphere interaction by a low‐level jet

The department of Choco, on the Colombian Pacific coast experiences 8,000 to 13,000 mm of average annual precipitation. Lloro (5°30′N, 76°32′W, 120m) has received above 12,700 mm (1952–1960). Using the NCEP/NCAR Reanalysis data, we show that the ocean-land-atmosphere interaction over the easternmost fringe of the tropical Pacific, enhanced by the dynamics of a low-level westerly jet (“CHOCO”), contributes to explain the existence of such record-breaking hydrological region. Deep convection develops from low-level moisture convergence by the CHOCO jet, combined with high-level easterly trade winds, orographic lifting on the western Andes, low surface pressures and warm air. Precipitation is organized in mesoscale convective complexes, in turn dynamically linked to the jet. The strength of the CHOCO jet (centered at 5°N) is associated with the gradient of surface air temperatures between western Colombia and the Nino 1+2 region, thereby exhibiting strong annual and interannual variability, which contributes to explaining Colombias hydro-climatology and its anomalies during ENSO.

Runoff generation and hydrologic response via channel network geomorphology — Recent progress and open problems

Abstract Recent theoretical emphasis on quantifying the processes of runoff generation in space-time in river basins has given a new focus to the fundamental importance of channel network geomorphology in river basin hydrology. Of particular significance in this context is the need for a comprehensive quantitative theory of channel networks in three dimensions reflecting the constraints of space filling and available potential energy as well as climatic, hydrologic and geologic controls which are in dynamical equilibrium with channel network forms. Recent progress related to these issues is discussed in a nontechnical way and illustrated with examples, and important open problems are identified.

The diurnal cycle of precipitation in the Tropical Andes of Colombia

Abstract Using hourly records from 51 rain gauges, spanning between 22 and 28 yr, the authors study the diurnal cycle of precipitation over the tropical Andes of Colombia. Analyses are developed for the seasonal march of the diurnal cycle and its interannual variability during the two phases of El Nino–Southern Oscillation (ENSO). Also, the diurnal cycle is analyzed at intra-annual time scales, associated with the westerly and easterly phases of the Madden–Julian oscillation, as well as higher-frequency variability (<10 days), mainly associated with tropical easterly wave activity during ENSO contrasting years. Five major general patterns are identified: (i) precipitation exhibits clear-cut diurnal (24 h) and semidiurnal (12 h) cycles; (ii) the minimum of daily precipitation is found during the morning hours (0900–1100 LST) regardless of season or location; (iii) a predominant afternoon peak is found over northeastern and western Colombia; (iv) over the western flank of the central Andes, precipitation ma...

The Hurst Effect: The Scale of Fluctuation Approach

After more than 40 years the so-called Hurst effect remains an open problem in stochastic hydrology. Historically, its existence has been explained either by preasymptotic behavior of the rescaled adjusted range R*n, certain classes of nonstationari ty in time series, infinite memory, or erroneous estimation of the Hurst exponent. Various statistical tests to determine whether an observed time series exhibits the Hurst effect are presented. The tests are based on the fact that for the family of processes in the Brownian domain of attraction, R*n/((0n))1/2 converges in distribution to a nondegenerate random variable with known distribution (functional central limit theorem). The scale of fluctuation 0, defined as the sum of the correlation function, plays a key role. Application of the tests to several geophysical time series seems to indicate that they do not exhibit the Hurst effect, although those series have been used as examples of its existence, and furthermore the traditional pox diagram method to estimate the Hurst exponent gives values larger than 0.5. It turned out that the coefficient in the relation of/?* versus n, which is directly proportional to the scale of fluctuation, was more important than the exponent. The Hurst effect motivated the popularization of I//noises and related ideas of fractals and scaling. This work illustrates how delicate the procedures to deal with infinity must be.

Nonlinear Forecasting of River Flows in Colombia Based Upon ENSO and Its Associated Economic Value for Hydropower Generation

There is ample evidence of hydrologie variability at annual and interannual time scales over the northern regions of tropical South America. Hydroelectric power provides a cheap regional energy source, yielding over seventy percent of Colombia’s national energy annually. The El Penol scheme on the Nare River is the country’s largest providing roughly 14% of national production. The region is particularly susceptible to droughts during warm phases of ENSO, however stream flow inputs are also subject to a variety of regional and local factors other than ENSO, which may makes forecasting difficult. The identification of a model which permits the reliable incorporation of readily available ocean-atmosphere variables, and variables derived from standard forecasts, to a potentially non-linear prediction of monthly stream flows is crucial to the optimal operation of the reservoir. The MARS (Multiple Adaptive Regression Splines) model is calibrated to provide forecasts of monthly stream flows over the period 1956–86. The applicability of the forecast technique is discussed by reference to comparisons between observed and forecasted flows in a separate model validation series (1987–92). Reliability of the stream flow forecasting methodology is investigated over “forecast horizons” ranging from 3 to 12 months, and the potential economic value of incorporating the methodology into the operation of the national power generating system is illustrated.

Tree-dependent extreme values: the exponential case

The length of the main channel in a river network is viewed as an extreme value statisic L on a randomly weighted binary rooted tree having M sources. Questions of concern for hydrologic applications are formulated as the construction of an extreme value theory for a dependence which poses and interesting contrast to the classical independent theory. Our main result is that in the case of exponentially weighted trees, the conditional distribution of n −1/2 L given M=n is asymptotically distributed as the maximum of a Brownian excursion

Dynamical System Exploration of the Hurst Phenomenon in Simple Climate Models

Extreme Events an Geophysical Mon

A Rural Electrification Expansion Model

Abstract In Colombia, power companies with capacity greater than 100 MW pay royalties over gross sales for rural electrification programs. These contributions are collected by regional development corporations (RDC) with a jurisdiction over the area where the generation projects are located. To that end, the RDC need to define a plan for rural electrification in the regions. A mixed integer linear programming model was developed to define rural electrification programs for Colombian regions. In this model several objectives are considered. Objectives such as economic efficiency, minimum municipal electricity coverage, municipal electricity development priorities and some others are included in the model. The ϵ-constant multiobjective methodology is used to solve this problem in which the economic efficiency objective is used as the objective function and the other objectives are stated as constraints. In this case trade-off curves between objectives can be developed to show how much of one objective has to be sacrificed to improve the other objective. These trade-off curves are the main decision tool for decision makers. The proposed model is used to define a rural electrification program for a Colombian region. The trade-off curves show that the number of households covered with electricity diminish when, beside the economic efficiency objective, other objectives are considered. Some conclusions and recommendations are presented.