Rainfall Error Model Research Articles

A calibration method for SWMM to mitigate the impact of the structure defect without considering runoff on building walls

In this study, we propose a hypothesis that an automatic calibration framework can address modeling uncertainties in the Storm Water Management Model (SWMM) due to structural defects that result in the inability of the model to account for runoff generated on building walls from wind-driven rain. To test this hypothesis, we introduce a rainfall error model into the calibration framework to indirectly consider the effects of inclined wind-driven rain on building walls. We couple the optimization algorithm Differential Evolution Adaptive Metropolis (DREAM) with SWMM using newly developed API functions. To demonstrate the effectiveness of the framework, we conduct a case study in Guangzhou, China and assess the impacts of rainfall uncertainty on model parameter estimations and simulated runoff boundaries. The results show that the framework can improve the average Nash–Sutcliffe index of selected events by more than 5%. It also captures peak flow more accurately. This framework contributes to the theory of SWMM calibration by accounting for structural defects and considering rainfall uncertainty.

Incorporating IMERG satellite precipitation uncertainty into seasonal and peak streamflow predictions using the Hillslope Link hydrological model

In global applications and data sparse regions, which comprise most of the earth, hydrologic model-based flood monitoring relies on precipitation data from satellite multisensor precipitation products or numerical weather forecasts. However, these products often exhibit substantial errors during the meteorological conditions that lead to flooding, including extreme rainfall. The propagation of precipitation forcing errors to predicted runoff and streamflow is scale-dependent and requires an understanding of the autocorrelation structure of precipitation errors, since error autocorrelation impacts the accumulation of precipitation errors over space and time in hydrologic models. Previous efforts to account for satellite precipitation uncertainty in hydrologic models have demonstrated the potential for improving streamflow estimates; however, these efforts use satellite precipitation error models that rely heavily on ground reference data such as rain gages or weather radar and do not characterize the nonstationarity of precipitation error autocorrelation structures. This work evaluates a new method, the Space-Time Rainfall Error and Autocorrelation Model (STREAM), which stochastically generates possible true precipitation fields, as input to the Hillslope Link Model to generate ensemble streamflow estimates. Unlike previous error models, STREAM represents the nonstationary and anisotropic autocorrelation structure of satellite precipitation error and does not use any ground reference to do so. Ensemble streamflow predictions are compared with streamflow generated using satellite precipitation fields as well as a radar-gage precipitation dataset during peak flow events. Results demonstrate that this approach to accounting for precipitation uncertainty effectively characterizes the uncertainty in streamflow estimates and reduces the error of predicted streamflow. Streamflow ensembles forced by STREAM improve streamflow prediction nearly to the level obtained using ground-reference forcing data across basin sizes.

WITHDRAWN: Incorporating IMERG satellite precipitation uncertainty into seasonal and peak streamflow predictions using the Hillslope Link hydrological model

In global applications and data sparse regions, which comprise most of the earth, hydrologic model-based flood monitoring relies on precipitation data from satellite multisensor precipitation products or numerical weather forecasts. However, these products often exhibit substantial errors during the meteorological conditions that lead to flooding, including extreme rainfall. The propagation of precipitation forcing errors to predicted runoff and streamflow is scale-dependent and requires an understanding of the autocorrelation structure of precipitation errors, since error autocorrelation impacts the accumulation of precipitation errors over space and time in hydrologic models. Previous efforts to account for satellite precipitation uncertainty in hydrologic models have demonstrated the potential for improving streamflow estimates; however, these efforts use satellite precipitation error models that rely heavily on ground reference data such as rain gages or weather radar and do not characterize the nonstationarity of precipitation error autocorrelation structures. This work evaluates a new method, the Space-Time Rainfall Error and Autocorrelation Model (STREAM), which stochastically generates possible true precipitation fields, as input to the Hillslope Link Model to generate ensemble streamflow estimates. Unlike previous error models, STREAM represents the nonstationary and anisotropic autocorrelation structure of satellite precipitation error and does not use any ground reference to do so. Ensemble streamflow predictions are compared with streamflow generated using satellite precipitation fields as well as a radar-gage precipitation dataset during peak flow events. Results demonstrate that this approach to accounting for precipitation uncertainty effectively characterizes the uncertainty in streamflow estimates and reduces the error of predicted streamflow. Streamflow ensembles forced by STREAM improve streamflow prediction nearly to the level obtained using ground-reference forcing data across basin sizes.

Ensemble Representation of Satellite Precipitation Uncertainty Using a Nonstationary, Anisotropic Autocorrelation Model

AbstractThe usefulness of satellite multi‐sensor precipitation (SMP) and other satellite‐informed precipitation products in water resources modeling can be hindered by substantial errors which vary considerably with spatiotemporal scale. One approach to cope with these errors is to combine SMPs with ensemble generation methods, such that each ensemble member reflects one plausible realization of the true—but unknown—precipitation. This requires replicating the spatiotemporal autocorrelation structure of SMP errors. The climatology of this structure is unknown for most locations due to a lack of ground‐reference observations, while the unique anisotropy and nonstationarity within any particular precipitation system limit the relevance of this climatology to the depiction of individual storm systems. Characterizing and simulating autocorrelation across spatiotemporal scales has thus been called a grand challenge within the precipitation community. We introduce the Space‐Time Rainfall Error and Autocorrelation Model (STREAM), which combines uncalibrated, anisotropic and nonstationary SMP spatiotemporal correlation modeling with a pixel‐scale precipitation error model to stochastically generate ensemble precipitation fields that resemble “ground truth” precipitation. We generate STREAM precipitation ensembles at high resolution (1‐hr, 0.1°) and evaluate these ensembles at multiple scales. STREAM ensembles consistently bracket ground‐truth observations and replicate the autocorrelation structure of ground‐truth precipitation fields. STREAM is compatible with pixel‐scale error/uncertainty formulations beyond those presented here, and could be applied to other precipitation sources such as numerical weather predictions or blended products. Although ground truth is used here to parameterize pixel‐scale uncertainty, if combined with other recent work in SMP uncertainty characterization, STREAM could be used without any ground data.

Impact of sampling of GPM orbital data on streamflow simulations

Global precipitation estimation depends on constellations of mainly passive microwave sensors along with satellite radars and constellations of geosynchronous earth orbit infrared sensors. With passive microwave constellations, a persisting challenge is the limited sampling, which impacts applications such as hydrological modeling. This study presents a framework to examine the impact of the Global Precipitation Measurement (GPM) orbital sampling on streamflow simulations. Orbital data from the GPM Dual Precipitation Radar (DPR) 2A-Ku is used within the Variable Infiltration Capacity (VIC) model to derive ensembles of runoff simulations. Ensembles of synthetic precipitation fields are generated at different sampling intervals which are representative of GPM orbital data products with the Satellite Rainfall Error Model (SREM-2D) over the Hirakud catchment in the Indian subcontinent over a period of two years (2015–2016). The NOAA-NCEP Climate Prediction Center (CPC) morphing technique (CMORPH) satellite-based gridded rainfall product is considered as the reference rainfall for our study. Sampling uncertainty in orbital precipitation data is shown to amplify in streamflow simulations. The statistical analysis indicates that increasing sampling rates tend to generate more realistic land surface fluxes. The results from our study indicate that streamflow simulations from VIC model using precipitation forcing at 6-hourly integration outperforms the simulations as compared to 3-hourly and 12-hourly forcing integration times. This is exemplified by the statistical indices, with mean relative error of 0.17 for simulations with 3-hourly forcing, 0.12 for simulation with 6-hourly forcing, and 0.57 for 12-hourly forcing. The relative Root-Mean-Square-Error (RMSE) for 3-hourly, 6-hourly, 12-hourly for 2015 are 0.31, 0.25, 1.43 and for 2016 are 0.25, 0.15, 1.06, respectively. It can be noticed that both mean relative error and relative RMSE show a similar pattern for both years. A generic framework is therefore proposed to study the manifestation of satellite constellation sampling uncertainty in hydrologic simulations, which are crucial for future missions such as the CubeSat-based Temporal Experiment for Storms and Tropical Systems, and the Time-Resolved Observations of precipitation structure and storm intensity with a constellation of smallsats.

Streamflow simulations using error correction ensembles of satellite rainfall products over the Huaihe river basin

This study aims to investigate the hydrologic applicability of an error correction method – SREM2D (two-dimensional stochastic satellite rainfall error model) to three satellite precipitation products in streamflow simulations. Three satellite precipitation products, including the Tropical Rainfall Measuring Mission (TRMM) Multiple-Satellite Precipitation Analysis (TMPA) real-time 3B42 product (3B42RT), the Climate Prediction Centre (CPC) morphing technique (CMORPH) gauge merged product (CMORPH BLD), and the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Network – Climate Data Record (PERSIANN CDR), are corrected using SREM2D. Over the upper Huaihe river basin, streamflow ensemble simulations are derived by forcing the distributed Variable Infiltration Capacity (VIC) model with the SREM2D-based rainfall ensemble.After applying SREM2D to satellite precipitation products, the streamflow simulations forced by TMPA 3B42RT and PERSIANN CDR rainfall ensembles are capable to capture flood peaks. However, the streamflow simulations forced by CMORPH BLD rainfall ensemble show poor performance for the extreme events, but exhibit good accuracy in non-flood flow simulation. The calibration of the model over the headwater subbasin betters the streamflow simulation, especially for reproducing extreme events during the main flood cases. Overall, SREM2D provides great potential to facilitate the application of satellite precipitation products in water management and decision making over Chinese river basins.

Improving the use of ground-based radar rainfall data for monitoring and predicting floods in the Iguaçu river basin

This study investigates the efficiency of correcting radar rainfall estimates using a stochastic error model in the upper Iguaçu river basin in Southern Brazil for improving streamflow simulations. The 2-Dimensional Satellite Rainfall Error Model (SREM2D) is adopted here and modified to account for topographic complexity, seasonality, and distance from the radar. SREM2D was used to correct the radar rainfall estimates and produce an ensemble of equally probable rainfall fields, that were then used to force a distributed hydrological model. Systematic and random errors in simulated streamflow were evaluated for a cascade of sub-basins of the Iguaçu catchment, with drainage area ranging from 1,808 to 21,536 km2). Results showed an improvement in the statistical metrics when the SREM2D ensemble was used as input to the hydrological model in place of the radar rainfall estimates in most sub-basins. Specifically, SREM2D was able to remove the relative bias (up to 50%) in the radar rainfall dataset regardless of the basin dimension, whereas the random error was reduced more prominently in the larger basins (up to 100 m3 s−1). An event scale evaluation was also performed for nine selected flood events in three sub-basins. SREM2D reduced the overestimation in the cumulative rainfall and streamflow volumes during these events.

Comparing the ensemble and extended Kalman filters for in situ soil moisture assimilation with contrasting conditions

Abstract. Two data assimilation (DA) methods are compared for their ability to produce an accurate soil moisture analysis using the Météo-France land surface model: (i) SEKF, a simplified extended Kalman filter, which uses a climatological background-error covariance, and (ii) EnSRF, the ensemble square root filter, which uses an ensemble background-error covariance and approximates random rainfall errors stochastically. In situ soil moisture observations at 5 cm depth are assimilated into the surface layer and 30 cm deep observations are used to evaluate the root-zone analysis on 12 sites in south-western France (SMOSMANIA network). These sites differ in terms of climate and soil texture. The two methods perform similarly and improve on the open loop. Both methods suffer from incorrect linear assumptions which are particularly degrading to the analysis during water-stressed conditions: the EnSRF by a dry bias and the SEKF by an over-sensitivity of the model Jacobian between the surface and the root-zone layers. These problems are less severe for the sites with wetter climates. A simple bias correction technique is tested on the EnSRF. Although this reduces the bias, it modifies the soil moisture fluxes and suppresses the ensemble spread, which degrades the analysis performance. However, the EnSRF flow-dependent background-error covariance evidently captures seasonal variability in the soil moisture errors and should exploit planned improvements in the model physics. Synthetic twin experiments demonstrate that when there is only a random component in the precipitation forcing errors, the correct stochastic representation of these errors enables the EnSRF to perform better than the SEKF. It might therefore be possible for the EnSRF to perform better than the SEKF with real data, if the rainfall uncertainty was accurately captured. However, the simple rainfall error model is not advantageous in our real experiments. More realistic rainfall error models are suggested.

Propagation of satellite precipitation uncertainties through a distributed hydrologic model: A case study in the Tocantins–Araguaia basin in Brazil

Summary This study investigates the applicability of error corrections to satellite-based precipitation products in streamflow simulations. A three-year time series (2008–2011) is considered across 19 sub-basins of the Tocantins–Araguaia basin (764,000 km 2 ), located in the center-north region of Brazil. A raingauge network (24 h accumulation) of approximately 300 collection points (∼1 gauge every 2500 km 2 ) is used as reference for evaluating the following four satellite rainfall products: the Tropical Rainfall Measuring Mission real-time 3B42 product (3B42RT), the Climate Prediction Center morphing technique (CMORPH), the Global Satellite Mapping of Precipitation (GSMaP), and the NOAA Hydroestimator (HYDRO-E). Ensemble streamflow simulations, for both dry and rainy seasons, are obtained by forcing the Distributed Hydrological Model developed by the Brazilian National Institute for Space Research (MHD–INPE) with the satellite rainfall products, corrected using a two-dimensional stochastic satellite rainfall error model (SREM2D). The ensemble simulations are evaluated using streamflow output derived by forcing the model with reference rainfall gauge data. SREM2D is able to correct for errors in the satellite precipitation data by pushing the modeled streamflow ensemble closer to the reference river discharge, when compared to the simulations forced with uncorrected rainfall input. Ensemble streamflow error statistics (MAE and RMSE) show a decreasing trend as a function of the catchment area for all satellite products, but the rainfall-to-streamflow error propagation does not show any dependence on the basin size.

Incorporating Surface Soil Moisture Information in Error Modeling of TRMM Passive Microwave Rainfall

This study assesses the significance of conditioning the error modeling of The National Aeronautics and Space Administration (NASA)'s Tropical Rainfall Measurement Mission Microwave Imager rainfall algorithm (2A12) to near-surface soil moisture data derived from a land surface model. The term “conditioning” means the model parameters' dependence on soil wetness. The Oklahoma (OK) region is used as the study area due to its relatively low vegetation and smooth terrain and the availability of high-quality in situ hydrometeorological data from the Mesonet network. The study period includes two warm seasons (March to October) from 2009 and 2010. The National Oceanic and Atmospheric Administration/National Severe Storms Laboratory ground radar-based National Mosaic and Quantitative Precipitation Estimation system (NMQ/Q2) is used as high-resolution (5-min/1-km) reference rainfall. The surface wetness conditions (wet, dry, and normal) were determined from surface soil moisture fields simulated by the NASA Catchment Land Surface Model forced with Q2 rainfall fields. A 2-D satellite rainfall error model, SREM2D, is used to provide the ensemble error representation of 2A12 rainfall using two different parameter calibration approaches: conditioning the SREM2D parameters to the surface soil wetness categories versus not. The statistical analysis of model-generated ensembles and associated error metrics show better performance when surface wetness information is used in SREM2D. In terms of quantification, the ensemble rainfall from the conditional SREM2D parameter calibration shows better reference rainfall encapsulation. The conditioning of SREM2D to soil wetness can apply to rainfall rate estimates from other microwave sensors on board low Earth orbiting satellites and is valuable for the forthcoming missions on precipitation (Global Precipitation Measurement) and soil moisture (Soil Moisture Active Passive).

Comparison of two model based approaches for areal rainfall estimation in urban hydrology

We introduce and compare two different approaches to estimate mean areal rainfall intensity in urban catchments. Both methods are based on the same lumped hydrological model that is calibrated beforehand. The first method uses a reverse model, i.e. an inverse formulation of a rainfall–runoff model. Rainfall intensities and their uncertainties are estimated from runoff data only. The second method estimates parameters of a rainfall error model using a Bayesian approach. It requires measurements of both runoff and rainfall. Although the two approaches are conceptually rather different, they address the same issue – the quantification of areal rainfall intensities and their related measurement errors – and a comparison is hence of interest. The merits and faults of the two methods are discussed. Results show that both methods provide best estimates of hyetographs with maximum intensities and total depths in a realistic order of magnitude, whereas the uncertainty of rainfall estimated with the reverse model is rather large.

Investigating the Applicability of Error Correction Ensembles of Satellite Rainfall Products in River Flow Simulations

Abstract This study uses a stochastic ensemble-based representation of satellite rainfall error to predict the propagation in flood simulation of three quasi-global-scale satellite rainfall products across a range of basin scales. The study is conducted on the Tar-Pamlico River basin in the southeastern United States based on 2 years of data (2004 and 2006). The NWS Multisensor Precipitation Estimator (MPE) dataset is used as the reference for evaluating three satellite rainfall products: the Tropical Rainfall Measuring Mission (TRMM) real-time 3B42 product (3B42RT), the Climate Prediction Center morphing technique (CMORPH), and the Precipitation Estimation from Remotely Sensed Imagery Using Artificial Neural Networks–Cloud Classification System (PERSIANN-CCS). Both ground-measured runoff and streamflow simulations, derived from the NWS Research Distributed Hydrologic Model forced with the MPE dataset, are used as benchmarks to evaluate ensemble streamflow simulations obtained by forcing the model with satellite rainfall corrected using stochastic error simulations from a two-dimensional satellite rainfall error model (SREM2D). The ability of the SREM2D ensemble error corrections to improve satellite rainfall-driven runoff simulations and to characterize the error variability of those simulations is evaluated. It is shown that by applying the SREM2D error ensemble to satellite rainfall, the simulated runoff ensemble is able to envelope both the reference runoff simulation and observed streamflow. The best (uncorrected) product is 3B42RT, but after applying SREM2D, CMORPH becomes the most accurate of the three products in the prediction of runoff variability. The impact of spatial resolution on the rainfall-to-runoff error propagation is also evaluated for a cascade of basin scales (500–5000 km2). Results show a doubling in the bias from rainfall to runoff at all basin scales. Significant dependency to catchment area is exhibited for the random error propagation component.

The Efficiency of Assimilating Satellite Soil Moisture Retrievals in a Land Data Assimilation System Using Different Rainfall Error Models

Abstract The efficiency of assimilating near-surface soil moisture retrievals from Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) observations in a Land Data Assimilation System (LDAS) is assessed using satellite rainfall forcing and two different satellite rainfall error models: a complex, multidimensional satellite rainfall error model (SREM2D) and the simpler (control) model (CTRL) used in the NASA Goddard Earth Observing System Model, version 5 LDAS. For the study domain of Oklahoma, LDAS soil moisture estimates improve over the satellite retrievals and the open-loop (no assimilation) land surface model estimates, exhibiting higher daily anomaly correlation coefficients (e.g., 0.36 in the open loop, 0.38 in the AMSR-E, and 0.50 in LDAS for surface soil moisture). The LDAS soil moisture estimates also match the performance of a benchmark model simulation forced with high-quality radar precipitation. Compared to using the CTRL rainfall error model in LDAS, using the more complex SREM2D exhibits only slight improvements in soil moisture estimates.

The Impact of Rainfall Error Characterization on the Estimation of Soil Moisture Fields in a Land Data Assimilation System

Abstract This study presents a numerical experiment to assess the impact of satellite rainfall error structure on the efficiency of assimilating near-surface soil moisture observations. Specifically, the study contrasts a multidimensional satellite rainfall error model (SREM2D) to a simpler rainfall error model (CTRL) currently used to generate rainfall ensembles as part of the ensemble-based land data assimilation system developed at the NASA Global Modeling and Assimilation Office. The study is conducted in the Oklahoma region using rainfall data from a NOAA multisatellite global rainfall product [the Climate Prediction Center (CPC) morphing technique (CMORPH)] and the National Weather Service rain gauge–calibrated radar rainfall product [Weather Surveillance Radar-1988 Doppler (WSR-88D)] representing the “uncertain” and “reference” model rainfall forcing, respectively. Soil moisture simulations using the Catchment land surface model (CLSM), obtained by forcing the model with reference rainfall, are randomly perturbed to represent satellite retrieval uncertainty, and assimilated into CLSM as synthetic near-surface soil moisture observations. The assimilation estimates show improved performance metrics, exhibiting higher anomaly correlation coefficients (e.g., ~0.79 and ~0.90 in the SREM2D nonassimilation and assimilation experiments for root zone soil moisture, respectively) and lower root-mean-square errors (e.g., ~0.034 m3 m−3 and ~0.024 m3 m−3 in the SREM2D nonassimilation and assimilation experiments for root zone soil moisture, respectively). The more elaborate rainfall error model in the assimilation system leads to slightly improved assimilation estimates. In particular, the relative enhancement due to SREM2D over CTRL is larger for root zone soil moisture and in wetter rainfall conditions.

The Effect of Satellite Rainfall Error Modeling on Soil Moisture Prediction Uncertainty

Abstract This study assesses the impact of satellite rainfall error structure on soil moisture simulations with the NASA Catchment land surface model. Specifically, the study contrasts a complex satellite rainfall error model (SREM2D) with the standard rainfall error model used to generate ensembles of rainfall fields as part of the Land Data Assimilation System (LDAS) developed at the NASA Global Modeling and Assimilation Office. The study is conducted in the Oklahoma region, which offers good coverage by weather radars and in situ meteorological and soil moisture measurement stations. The authors used high-resolution (25 km, 3-hourly) satellite rainfall fields derived from the NOAA/Climate Prediction Center morphing (CMORPH) global satellite product and rain gauge–calibrated radar rainfall fields (considered as the reference rainfall). The LDAS simulations are evaluated in terms of rainfall and soil moisture error. Comparisons of rainfall ensembles generated by SREM2D and LDAS against reference rainfall show that both rainfall error models preserve the satellite rainfall error characteristics across a range of spatial scales. The error structure in SREM2D is shown to generate rainfall replicates with higher variability that better envelop the reference rainfall than those generated by the LDAS error model. Likewise, the SREM2D-generated soil moisture ensemble shows slightly higher spread than the LDAS-generated ensemble and thus better encapsulates the reference soil moisture. Soil moisture errors, however, are less sensitive than precipitation errors to the complexity of the precipitation error modeling approach because soil moisture dynamics are dissipative and nonlinear.

Rainfall uncertainty in hydrological modelling: An evaluation of multiplicative error models

Summary This paper presents an investigation of rainfall error models used in hydrological model calibration and prediction. Traditional calibration methods assume input error to be negligible: an assumption which can lead to bias in parameter estimation and compromise model predictions. In response, a growing number of studies now specify an error model for rainfall input, usually simple in form due to both difficulties in understanding sampling errors in rainfall, and to computational constraints during parameter estimation. Such rainfall error models have not typically been validated against experimental evidence. In this study we use data from a dense gauge/radar network in the Mahurangi catchment (New Zealand) to directly evaluate the form of basic statistical rainfall error models. For this catchment, our results confirm the suitability of a multiplicative error formulation for correcting mean catchment rainfall values during high-rainfall periods (e.g., intensities over 1 mm/h); or for longer timesteps at any rainfall intensity (timestep 1 day or greater). We show that the popular lognormal multiplier distribution provides a relatively close approximation to the true error characteristics but does not capture the distribution tails, especially during heavy rainfall where input errors would have important consequences for runoff prediction. Our research highlights the dependency of rainfall error structure on the data timestep.

Understanding the Scale Relationships of Uncertainty Propagation of Satellite Rainfall through a Distributed Hydrologic Model

Abstract The study presents a data-based numerical experiment performed to understand the scale relationships of the error propagation of satellite rainfall for flood evaluation applications in complex terrain basins. A satellite rainfall error model is devised to generate rainfall ensembles based on two satellite products with different retrieval accuracies and space–time resolutions. The generated ensembles are propagated through a distributed physics-based hydrologic model to simulate the rainfall–runoff processes at different basin scales. The resulted hydrographs are compared against the hydrograph obtained by using high-resolution radar rainfall as the “reference” rainfall input. The error propagation of rainfall to stream runoff is evaluated for a number of basin scales ranging between 100 and 1200 km2. The results from this study show that (i) use of satellite rainfall for flood simulation depends strongly on the scale of application (catchment area) and the satellite product resolution, (ii) different satellite products perform differently in terms of hydrologic error propagation, and (iii) the propagation of error depends on the basin size; for example, this study shows that small watersheds (<400 km2) exhibit a higher ability in dampening the error from rainfall to runoff than larger-sized watersheds, although the actual error increases as drainage area decreases.

Inference of Spatial Scaling Properties of Rainfall: Impact of Radar Rainfall Estimation Uncertainties

The existence of relationships able to connect quantities across different spatio-temporal scales represents an attractive way of describing and characterizing the high spatial and temporal variability of the rainfall process. Several studies investigated the scaling properties of spatial rainfall, and in most of the cases, these analyses were performed using radar-based estimates of rainfall, which are notoriously affected by systematic and random uncertainties. The impact of these errors on the estimated scaling properties of spatial rainfall still remains an open question. By using an empirically based radar rainfall error model, the authors explore this issue by generating ensembles of probable true rainfall fields, conditioned on radar rainfall maps. Fifteen rainfall events over Oklahoma are analyzed, and it is shown how the presence of radar rainfall errors results in biased estimates of the scaling properties of rainfall.

Satellite Rainfall Uncertainty Estimation Using an Artificial Neural Network

Abstract This paper describes a neural network–based approach to estimate the conditional distribution function (cdf) of rainfall with respect to multidimensional satellite-derived input data. The methodology [Conditional Histogram of Precipitation (CHIP)] employs a histogram-based approximation of the cdf. In addition to the conditional expected rainfall rate, it provides conditional probabilities for that rate falling within each of a fixed set of intervals or bins. A test algorithm based on the CHIP approach was calibrated against Goddard profiling algorithm (GPROF) rainfall data for June–August 2002 and then used to produce a 30-min, 0.5° rainfall product from global (60°N–60°S) composite geostationary thermal infrared imagery for June–August 2003. Estimated rainfall rates and conditional probabilities were validated against 2003 GPROF data. The CHIP methodology provides the means to extend existing probabilistic and ensemble satellite rainfall error models, conditioned on a single, scalar, satellite rainfall predictor or upon scalar rainfall-rate outputs, to make full use of multidimensional input data.

Correction to "A two-dimensional satellite rainfall error model"

Two corrections to the above-named article [ibid., vol. 44, no. 6, pp. 1511¿ 1522, Jun. 2006] are indicated here. They are, respectively, to the biography for author F. Hossain and to reference [17].