James C. I. Dooge

A simple model for estimating the sensitivity of runoff to long-term changes in precipitation without a change in vegetation

Abstract Forecasts of changes in precipitation (P) and potential evaporation (PE) can be applied to hydrologic models calibrated on existing conditions to obtain predictions of changes in runoff. This study describes an alternative approach, which uses a simple soil-moisture accounting model with a small number of independent and physically based parameters to explore the sensitivity of runoff to climate change for three simplified climates. The climate types chosen initially are those for which a piecewise analytical solution can be obtained so that computer programmes involving numerical solutions can be verified before being applied to field data. Sensitivity factors are calculated for the various cases and their relationships with climatic conditions and soil conditions are explored. Breakpoint values were determined for each type of climate studied. These correspond to situations in which the soil becomes momentarily saturated once during the seasonal cycle but does not remain saturated for any finite duration. For humidity ratios greater than the breakpoint, the sensitivity of runoff to precipitation increases abruptly. For the climates studied, the sensitivity factor approaches the value of the soil parameter c as the humidity index approaches zero. The other climates studied exhibit the same sensitivity at this limit. A particular feature of the model is that analytical solutions can be determined in many cases to check and confirm the results of the numerical simulations.

Hydrodynamic derivation of storage parameters of the Muskingum model

Abstract The St. Venant equations for unsteady flow in open channels and the Muskingum method are written both in their conventional forms and in the state-space formulation. The hydrodynamic equation of motion is solved by the method of state trajectory variation and the result for the first-order variation in the state-space variables is used as a basis of linking the parameters of the Muskingum model with the hydraulic parameters of the open channel reach. The results are applicable to any shape of cross-section and to any type of friction law.

An efficient and robust method for estimating unit hydrograph ordinates

Abstract The coefficient matrix for the “normal equations” for least-squares estimates of discrete unit hydrographs (DUH) is symmetric Toeplitz. This paper describes how to take advantage of this matrix structure to reduce both the data storage and arithmetic computation requirements of computer programs for estimating DUHs. The method is particularly useful for small computers when memory space is limited or when large amounts of data are involved. The algorithm can be used to provide smoothed least-squares estimates of the DUH using a single extra arithmetic addition. Estimates of DUHs for multiple-event data can easily be calculated. Computer programs are presented for both the single-event and multiple-event case. The utility of the smoothed estimates is illustrated using real data which would give unrealistic ordinary least-squares estimates.

The shape parameters of the geomorphologic unit hydrograph

Abstract Numerical experiments are carried out to explore: (a) the relationship between the dimensionless third moment and the dimensionless second moment of the classical geomorphologic unit hydrograph; (b) the sensitivity of this shape indicator to the assumption in the GUH model relating the delay time in a stream segment to some power of the segment length; (c) the relationship between the parameters of the GUH and the geomorphic parameters of the catchment. In the paper, the geomorphologic unit hydrograph is formulated on a deterministic basis in contrast to the Markov and the statistical mechanics approaches.

Partial Analysis Applied to Scale Problems in Surface Moisture Fluxes

Partial analysis is applied to the problem of predicting the moisture fluxes of infiltraton and evaporation at land surfaces. The discussion covers the widely different scales of the soil particle, a soil pedon, a field, a basin and a biome. It is suggested that simplified models can be used at these different scales to provide bounding solutions to the integrated behaviour of land surface fluxes of interest in linking hydrologic models and general circulation climate models.

Hydrology in perspective

Abstract Scientific hydrology is considered against the background of the classical development of scientific knowledge, and applied hydrology is considered in the context of the many diverse factors relevant to providing water for health and for food throughout the world.

Searching for Simplicity in Hydrology

The use of simplification as a route to scientific insight is reviewed with examples from hydrology and analogies from other sciences. The discussion covers a number of types of simplification: (a) simplification of the governing equations; (b) reduction of the state space, i.e. the number of dependent variables; (c) reduction of the solution space, i.e. the number of independent variables; (d) reduction of the parameter space, e.g. by freezing a slowly varying parameter; (e) simplification of the driving function e.g. Fourier analysis. The importance of scale is stressed and the possibility of apparent paradoxes between differing scales is noted. The complementary nature of deterministic and stochastic approaches is also discussed.

SCALING EFFECTS ON MOISTURE FLUXES AT UNVEGETATED LAND SURFACES

As part of a larger study on spatial variability of land surface processes, the authors explore the sensitivity of land surface modules for climate models to the method of simulating the unsaturated subsurface flows. By examining the behavior of a number of different subsurface modules, it is shown that the surface fluxes, and consequently the water balance throughout the year, vary widely for different simulations of subsurface conditions. Typical results are presented for a specified climates and soil types. In order to reduce the complexity and computation time for the subsequent sensitivity studies, it is shown that a linearized module displays the range of behavior expected in practice. For given forcing functions of precipitation and potential evaporation, varying the depth of the modelled soil layer and changing the lower boundary conditions greatly influence the annual values of the components of the water balance. Monte Carlo simulations are used to demonstrate that spatial variation in soil properties produces large variation in runoff and compensating variations in deep drainage with a much smaller variation in evaporation. Finally, it is shown that for a given coefficient of variation in soil scaling properties, the effect on the effective large-scale sorptivity is insensitive to the type of statistical distribution used to describe the variation.

Unit hydrograph estimation with multiple events and prior information: I. Theory and a computer program

Abstract The method of regularization for estimating unit hydrographs is expanded to allow the inclusion of prior information about the unit hydrograph shape. This may give smooth estimates without any loss in volume. The method is illustrated with prior information from a regression on catchment characteristics and with catchment lag determined from the data. A computer program to implement the method is given together with a sample calculation.

The distributed Muskingum model

Abstract This paper investigates the limiting form of the multiple Muskingum model when the number of reaches increases to infinity, while maintaining finite values for the first and second moments. Both the cumulants, and the amplitude and phase characteristics of this distributed Muskingum model (DMM) are derived. The model is compared to the solution of the linearised Saint-Venant equation for a semi-infinite uniform channel (LSV). The error of the DMM in predicting the third central moment of the LSV is shown to be independent of channel length in contrast to the classical Muskingum model in which the error increases rapidly with length of channel.