Fred L. Ogden

Runoff sensitivity to temporal and spatial rainfall variability at runoff plane and small basin scales

Surface runoff sensitivity to spatial and temporal variability of rainfall is examined using physically based numerical runoff models. Rainfall duration tr and temporal sampling interval δt are varied systematically, and normalized by the time to equilibrium te. The relative sensitivity Rs is defined as the total volume of outflow variability over 50 Monte Carlo simulations normalized by the rainfall volume and the coefficient of variation of rainfall. Relative sensitivity to temporal rainfall variability increases with both tr and δt. An asymptotic Rs value proportional to (δt/te1/2) is approached as tr ≫ te. Two-dimensional surface runoff simulations with spatially variable rainfall, without temporal variability, on two watersheds indicate that Rs decreases as tr/te increases. Normalized Rs versus tr/te curves are identical for two watersheds and a one-dimensional overland flow plane. These findings indicate that spatial variability is dominant when tr te, particularly for larger values of δt/te.

On the calibration and verification of two-dimensional, distributed, Hortonian, continuous watershed models.

Physically based, two-dimensional, distributed parameter Hortonian hydrologic models are sensitive to a number of spatially varied parameters and inputs and are particularly sensitive to the initial soil moisture field. However, soil moisture data are generally unavailable for most catchments. Given an erroneous initial soil moisture field, single-event calibrations are easily achieved using different combinations of model parameters, including physically unrealistic values. Verification of single-event calibrations is very difficult for models of this type because of parameter estimation errors that arise from initial soil moisture field uncertainty. The purpose of this study is to determine if the likelihood of obtaining a verifiable calibration increases when a continuous flow record, consisting of multiple runoff producing events is used for model calibration. The physically based, two-dimensional, distributed, Hortonian hydrologic model CASC2D [Julien et al., 1995] is converted to a continuous formulation that simulates the temporal evolution of soil moisture between rainfall events. Calibration is performed using 6 weeks of record from the 21.3 km 2 Goodwin Creek Experimental Watershed, located in northern Mississippi. Model parameters are assigned based on soil textures, land use/land cover maps, and a combination of both. The sensitivity of the new model formulation to parameter variation is evaluated. Calibration is performed using the shuffled complex evolution method [Duan et al., 1991]. Three different tests are conducted to evaluate model performance based on continuous calibration. Results show that calibration on a continuous basis significantly improves model performance for periods, or subcatchments, not used in calibration and the likelihood of obtaining realistic simulations of spatially varied catchment dynamics. The automated calibration reveals that the parameter assignment methodology used in this study results in overparameterization. Additional research is needed in spatially distributed hydrologic model parameter assignment methodologies for hydrologic forecasting.

Runoff model sensitivity to radar rainfall resolution

Rainfall rates estimated from polarimetric weather radar measurements of a convective rainstorm are used as input to a two-dimensional physically based rainfall-runoff model. The correlation length of the input rainfall field LS is 2.3 km. Runoff simulations are performed on two semi-arid watersheds covering 32 km2 and 121 km2 at basin data grid sizes LM of 125 m and 200 m, respectively. The characteristic basin length scale LW is taken as the square root of the watershed area. Rainfall data at resolutions LR of 1, 2, 3, 4, 6 and 8 km serve as model input to determine the effect of precipitation data spatial resolution on computed outflow hydrographs. Two dimensionless length parameters are identified which describe the similarity of the effect of rainfall data aggregation on both basins. The first parameter, LRLS, describes ‘storm smearing’, and the second parameter, LRLW, describes ‘watershed smearing’. Results from simulations without infiltration show storm smearing occurring as LR → LS. Watershed smearing causes more significant deviations from simulations using the finest-resolution data when LRLW exceeds 0.4. Results with infiltration reveal that excess rainfall volumes decrease with increasing LRLW. Additionally, excess rainfall volumes do not converge as LRLW is decreased to the practical lower limit provided by contemporary weather radars, which is of the order of 1 km.

Similarity in Catchment Response: 1. Stationary Rainstorms

The variability in Hortonian surface runoff discharge and volume produced by stationary rainstorms on watersheds with spatially distributed soil saturated hydraulic conductivity is examined using a two-dimensional runoff model and a Monte Carlo methodology. Results indicate that rainfall duration tr, rainfall intensity i, representative time to equilibrium tre, mean saturated hydraulic conductivityKm, and coefficient of variation Cυ play major roles in the variability of surface runoff. Similarity in surface runoff generated on heterogeneous soils is governed by the following dimensionless parameters: T* = tr/tre, K* = Km/i, and Cυ. The variability in both discharge and runoff volume for randomly distributed systems increases with K* and Cυ, compared to the runoff generated from uniformly distributed systems. Runoff variability decreases whenT* increases unless the mean value of hydraulic conductivity approaches the rainfall intensity (K* → 1). In highly pervious watersheds the steady state discharge depends on the spatial distribution of hydraulic conductivity. Lumped values of saturated hydraulic conductivity are found to typically underestimate the peak discharge and runoff volume.

Similarity in Catchment Response: 2. Moving Rainstorms

The influence of storm motion on runoff is explored, with a focus on dimensionless hydrologic similarity parameters. One- and two-dimensional physically based runoff models are subjected to moving rainstorms. A dimensionless storm speed parameterUte/Lp, where U is the storm speed, te is the runoff plane kinematic time to equilibrium, and Lp is the length of the runoff plane, is identified as a similarity condition. Storm motion effects on the peak discharge are greatest when the storm is traversing a one-dimensional runoff plane in the downslope direction at a dimensionless speed of Ute/Lp = 0.5. This conclusion holds for all values of the dimensionless storm sizes Ls/Lp where Ls is the length of the storm in the direction of motion. Simulations with a two-dimensional rainfall-runoff model confirm the applicability of this similarity parameter on natural watershed topography. Results indicate that the detailed simulation of storm motion is necessary when the storm is moving near the velocity of maximum effect, which is considerably slower than typical storm velocities.

Saturated area formation on nonconvergent hillslope topography with shallow soils: a numerical investigation.

Prediction of saturated area formation is important for hydrologic modeling of watersheds with shallow, highly pervious soils. This simulation study examines the relative importance of hillslope properties and rainfall rate on the evolution of saturated source areas during wetting. The study focuses on homogeneous, nonconvergent hillslope topography with constant slope. The two-dimensional, variably saturated groundwater model VS2D [Healy, 1990; Lappala et al. 1993] is used to simulate saturated area formation under the action of steady uniform rainfall. The study methodology systematically varies four hillslope properties, depth to impervious layer, slope length, slope angle, and average saturated hydraulic conductivity, and the rainfall rate. Results indicate that the fraction of the hillslope length that is saturated at equilibrium is a function of a parameter Φ, which is defined as the rainfall rate multiplied by the slope length, divided by the slope angle, soil thickness, and saturated hydraulic conductivity. The temporal evolution of saturated area is analyzed in terms of the equilibrium time. Nonlinearity in the unsaturated zone and differences in hillslope properties result in a nonunique time to equilibrium relation. The time to equilibrium is maximum when factors that tend to cause surface saturation are in approximate balance with those that tend to dissipate surface saturation. The temporal evolution of surface saturation during wetting follows a wide variety of trajectories. Equivalent hillslope soil water storage ratios on slopes with different properties can result in a wide range of surface saturation conditions. Hillslopes with shallower soils and smaller slope angles are most susceptible to saturated area formation. However, sudden changes in surface saturation are possible on steep hillslopes when 1 < Φ < 6.

An Experimental Study of Small-Scale Variability of Radar Reflectivity Using Disdrometer Observations

Abstract Analysis of data collected by four disdrometers deployed in a 1-km2 area is presented with the intent of quantifying the spatial variability of radar reflectivity at small spatial scales. Spatial variability of radar reflectivity within the radar beam is a key source of error in radar-rainfall estimation because of the assumption that drops are uniformly distributed within the radar-sensing volume. Common experience tells one that, in fact, drops are not uniformly distributed, and, although some work has been done to examine the small-scale spatial variability of rain rates, little experimental work has been done to explore the variability of radar reflectivity. The four disdrometers used for this study include a two-dimensional video disdrometer, an X-band radar-based disdrometer, an impact-type disdrometer, and an optical spectropluviometer. Although instrumental differences were expected, the magnitude of these differences clouds the natural variability of interest. An algorithm is applied to ...

Statistical Analysis of Radar Rainfall Error Propagation

Abstract The prediction uncertainty of a hydrologic model is closely related to model formulation and the uncertainties in model parameters and inputs. Currently, the foremost challenges concern not only whether hydrologic model outputs match observations, but also whether or not model predictions are meaningful and useful in the contexts of land use and climate change. The latter is difficult to determine given that model inputs, such as rainfall, have errors and uncertainties that cannot be entirely eliminated. In this paper the physically based simulation methodology developed by Sharif et al. is used to expand this investigation of the propagation of radar rainfall estimation errors in hydrologic simulations. The methodology includes a physics-based mesoscale atmospheric model, a three-dimensional radar simulator, and a two-dimensional infiltration-excess hydrologic model. A time series of simulated three-dimensional precipitation fields over a large domain and a small study watershed are used, which ...

Radar studies of heavy convective rainfall in mountainous terrain

Heavy rainfall, topography, storm motion, and storm evolution are closely linked for four storms that produced catastrophic flooding along the Front Range of the Rocky Mountains and the east slope of the Blue Ridge Mountains. Storms selected for detailed study in this paper are the Rapidan storm of June 27, 1995, the Fort Collins storm of July 28, 1997, the Buffalo Creek storm of July 12, 1996, and the Monocacy storm of June 18, 1996. The Buffalo Creek storm and the Fort Collins storm occurred in the Front Range of the Rocky Mountains in Colorado; the Rapidan and Monocacy storms occurred along the east slopes of the Blue Ridge of Virginia and southern Pennsylvania. The four storms caused catastrophic flooding at drainage basin scales between 1 and 1000 km 2 . The scale of flood response for these events imposes a need to characterize rainfall variability at very fine space scales and timescales, of the order of 1 km spatial scale and 1-5 min timescale. A fundamental issue for the hydrometeorology of extreme rainfall in mountainous terrain is whether anomalously large rainfall accumulations in orographic convection result from anomalously slow net storm motion, anomalously large rainfall rates, or both. Anomalous storm motion and processes resulting in catastrophic rainfall rates are examined for each of the four storms. Of particular importance for anomalous storm motion in orographic convection are interactions between the low-level wind field and terrain features.

Comparison of Two Raindrop Size Distribution Retrieval Algorithms for X-Band Dual Polarization Observations

In this study the authors evaluate two algorithms, the so-called beta () and constrained methods, proposed for retrieving the governing parameters of the “normalized” gamma drop size distribution (DSD) from dual-polarization radar measurements. The method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (ZH), differential reflectivity (ZDR), and specific differential phase shift (KDP). The constrained method assumes that the axis-ratio relation is fixed and computes DSD parameters from ZH, ZDR, and an empirical relation between the DSD slope and shape parameters. The two techniques are evaluated for polarimetric X-band radar observations by comparing retrieved DSD parameters with disdrometer observations and examining simulated radar parameters for consistency. Error effects on the method and constrained method retrievals are analyzed. The approach is found to be sensitive to errors in KDP and to be less consistent with observations. Large retrieved values are found to be associated with large retrieved DSD shape parameters and small median drop diameters. The constrained method provides reasonable rain DSD retrievals that agree better with disdrometer observations.