Scaling of tropical rainfall as observed by TRMM precipitation radar

We used a three-year (1998–2000) dataset of TRMM Precipitation Radar observations to investigate the scaling properties of spatial rainfall fields. This dataset allows consideration of spatial scales ranging from about 4.3 km to 138 km and short temporal scales corresponding to the sensor overpasses. The focus is on the marginal spatial moment scaling, which allows estimation of the scaling parameters from a single scene of data. Here we present a global perspective of the scaling properties of tropical rainfall in terms of its spatial variability, atmospheric forcing, predictability, and applicability. Our results reveal the following: 1) the scaling parameters exhibit strong variability associated with land/ocean contrast and mean precipitation at the synoptic scale; 2) there exists a one-to-one relationship between the scaling parameters and the large-scale spatial average rain rate of a universal functional form; 3) the majority of the scenes are consistent with the hypothesis of scale invariance at the moment orders of 0 and 2; 4) relatively there are more scale-invariant rain scenes over land than over ocean; and 5) for the scenes that are non-scale-invariant, deviation from scale-invariance mainly arises from the increasingly intermittent behavior of rainfall as spatial scale decreases. These results have important implications for the development and calibration of downscaling procedures designed to reproduce rainfall properties at different spatial scales and lead to a better understanding of the nature of tropical rainfall at various spatial resolutions.     

Intercomparison of Sensible Heat Flux from Large Aperture Scintillometer and Eddy Covariance Methods: Field Experiment over a Homogeneous Semi-arid Region

Scintillometers are becoming increasingly popular for the validation of satellite remote sensing sensible heat-flux estimates due to the comparable spatial resolutions. However, it is important to gain confidence in the accuracy of the sensible heat-flux measurements obtained by the scintillometer. Large aperture scintillometer (LAS) and eddy-covariance (EC) measurements were collected over a homogeneous, dry and semi-arid region near Las Cruces, New Mexico, USA, where the homogeneity allowed direct comparison of the two instruments despite their differences in footprint sizes. The differences between the sensible heat-flux measured by both LAS and EC systems fall within the differences between two EC systems. We conclude that the large aperture scintillometer is a reliable system for measuring sensible heat flux in a dry semiarid region.     

Estimating actual rainfall from satellite rainfall products

The lack of uncertainty measures in operational satellite rainfall (SR) products leads to a situation where users of the SR products know that there are significant errors in the products, but they have no quantitative information about the distribution of these errors. The authors propose a semiparametric model to characterize the conditional distribution of actual rainfall (AR) given measures from SR products. The model consists of two components: a conditional gamma density given each SR, and a smooth functional relationship between the gamma parameters and SR. The model is developed for monthly rainfall, estimated from a satellite with sampling frequency once a day, averaged over an area of 512 × 512 km² in the Mississippi River basin. The conditional distribution results are more informative than deterministic SR products since the whole conditional distribution enables users to take appropriate actions according to their own risk assessments and cost/benefit analyses.     

Modeling distribution of temporal sampling errors in area-time-averaged rainfall estimates

In this paper, the authors examine models of probability distributions for sampling error in rainfall estimates obtained from discrete satellite sampling in time based on 5 years of 15-min radar rainfall data in the central United States. The sampling errors considered include all combinations of 3, 6, 12, or 24 h sampling of rainfall over 32, 64, 128, 256, or 512 km square domains, and 1, 5, or 30 day rainfall accumulations. Results of this study reveal that the sampling error distribution depends strongly on the rain rate; hence the conditional distribution of sampling error is more informative than its marginal distribution. The distribution of sampling error conditional on rain rate is strongly affected by the sampling interval. At sampling intervals of 3 or 6 h, the logistic distribution appears to fit the conditional sampling error quite well, while the shifted-gamma, shifted-weibull, shifted-lognormal, and normal distributions fit poorly. At sampling intervals of 12 or 24 h, the shifted-gamma, shifted-weibull, or shifted-lognormal distribution fit the conditional sampling error better than the logistics or normal distribution. These results are vital to understanding the accuracy of satellite rainfall products, for performing validation assessment of these products, and for analyzing the effects of rainfall-related errors in hydrological models.     

Parameter Estimation for Groundwater Models under Uncertain Irrigation Data

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.     

Incorporating landscape depression heterogeneity into the Soil and Water Assessment Tool (SWAT) using a probability distribution

Modelling the hydrology of North American Prairie watersheds is complicated because of the existence of numerous landscape depressions that vary in storage capacity. The Soil and Water Assessment Tool (SWAT) is a widely applied model for long‐term hydrological simulations in watersheds dominated by agricultural land uses. However, several studies show that the SWAT model has had limited success in handling prairie watersheds. In past works using SWAT, landscape depression storage heterogeneity has largely been neglected or lumped. In this study, a probability distributed model of depression storage is introduced into the SWAT model to better handle landscape storage heterogeneity. The work utilizes a probability density function to describe the spatial heterogeneity of the landscape depression storages that was developed from topographic characteristics. The integrated SWAT–PDLD model is tested using datasets for two prairie depression dominated watersheds in Canada: the Moose Jaw River watershed, Saskatchewan; and the Assiniboine River watershed, Saskatchewan. Simulation results were compared to observed streamflow using graphical and multiple statistical criterions. Representation of landscape depressions within SWAT using a probability distribution (SWAT–PDLD) provides improved estimations of streamflow for large prairie watersheds in comparison to results using a lumped, single storage approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Hydrological modelling of Ethiopian catchments using limited data

The hydrological component of the soil and water assessment tool (SWAT) model is adapted for two Ethiopian catchments based on primary knowledge of the coherence spectrum between rainfall and stream flow data. Spectrum analysis using the available nearby climatic data is made to limit the temporal and spatial scales (inverse rate coefficients) subject to the calibration of compartmentalized runoff models. The exclusion of unwarranted time scales in the calibration implies that the model efficiency (r² values) decrease only moderately between calibration and validation, and the optimization is focused on warranted problems. On the basis of the available data for the two Ethiopian catchments, the implication is that only periods longer than about 50 days can be reliably evaluated in the model. The model structure of SWAT for the surface runoff and groundwater flow response is modified to make the time scales consistent with the results of the spectrum analysis. An optimization algorithm is developed to constrain and combine the model parameters with the spectrum analysis results. Copyright © 2009 John Wiley & Sons, Ltd.     

Satellite remote sensing and conceptual cloud modeling for convective rainfall simulation

Motivated by the need for rainfall prediction models in data scarce areas, we adapted a simple storage based cloud model to use routinely available thermal infrared (TIR) data. The data is obtained from the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) of the Meteosat Second Generation (MSG-2) satellite. Model inputs are TIR cloud top temperatures at 15-min intervals and observations of pressure, temperature, and dew point temperatures from ground-based stations at 30-min intervals. The sensitivity of the parsimonious cloud model to its parameters is evaluated by a regional sensitivity analysis (RSA) which suggests that model performance is sensitive to few parameters. The model was calibrated and tested for four convective events that were observed during the wet season in the source basin of the Upper Blue Nile River. The difference between the simulated and the observed depth of the selected rain events varies between 0.2 and 1.8 mm with a root mean square error of smaller than 0.5 mm for each event. It is shown that the updraft velocity characteristic can provide relevant information for rainfall forecasting. The simulation results suggest the effectiveness of the model approach as evaluated by selected performance measures. The various characteristics of the rainfall events as simulated generally match to observed counter parts when ground-based and remote sensing observations are combined.     

Sub-daily scale validation of satellite-based high-resolution rainfall products

Recent research efforts have been geared towards developing high-resolution rainfall products from satellites for hydrological applications. A necessary step in assessing the potential and utility of these products is to quantify the uncertainty associated with them at validation scales appropriate for hydrological applications. The main objective of this paper is to evaluate the accuracy of the widely-known PERSIANN-CCS high-resolution (hourly, 0.04° × 0.04°) satellite rainfall products against high-quality NEXRAD radar rainfall observations in the Little Washita watershed. Our results reveal that (1) PERSIANN-CCS shows high skills in reproducing the patterns of inter-annual rainfall variability on a monthly basis; (2) both at the hourly and storm scales, the performance statistics of PERSIANN-CCS exhibit large spread, suggesting that the quality of PERSIANN-CCS product is almost unique for each hour and storm; and (3) significant improvement in performance statistics is obtained as PERSIANN-CCS products are averaged to longer sub-daily time scales. The implications of our results are: (1) PERSIANN-CCS could be used with high confidence for inter-annual rainfall variability studies; (2) PERSIANN-CCS products need to be accompanied by corresponding hourly error estimates in order to provide meaningful error estimates for hydrological applications; and (3) research is needed to characterize the tradeoff between the quality of rainfall input and the space-time resolution of hydrological modeling, as a function of watershed size and hydrologic model complexity level.     

Hydraulic relationships between buried valley sediments of the glacial drift and adjacent bedrock formations in northeastern Ohio,USA

Buried valleys are ancient river or stream valleys that predate the recent glaciation and since have been filled with glacial till and/or outwash. Outwash deposits are known to store and transmit large amounts of groundwater. In addition to their intrinsic hydraulic properties, their productivity depends on their hydraulic relationships with the adjacent bedrock formations. These relationships are examined using a steady-state three-dimensional groundwater flow model through a section of a buried valley in northeastern Ohio, USA. The flow domain was divided into five hydrostratigraphic units: low-conductivity (K) till, high-K outwash, and three bedrock units (Pottsville Formation, Cuyahoga Group and Berea Sandstone). The model input was prepared using the data from well logs and drilling reports of residential water wells. The model was calibrated using observed heads with mean residual head error of 0.3 m. The calibrated model was used to quantify flux between the buried valley and bedrock formations. Mass balance was calculated to within an error of 2–3 %. Mass balance of the buried valley layer indicates that it receives 1.6 Mm³/year (≈40 % of the total inflow) from the adjacent bedrock aquifers: Pottsville Formation contributes 0.96 Mm³/year (60 %) while the Berea Sandstone 0.64 Mm³/year (40 %).