H33A-0964
Constructing Design Rainfall Hyetographs Using Trivariate Plackett Family of Copulas
Multivariate stochastic analyses via copulas are receiving increasing attention in the hydrologic literatures due to the flexibility they offer in construction of joint distributions with various combinations of marginals and dependence structures. Among the many choices of dependence models, the Frank family of Archimedean copulas has been popular for many bivariate problems. However, there are limitations to extending the application of copulas to trivariate and higher dimensions, namely difficulties in preserving all lower-level mutual dependencies and the compatibility problem in multivariate statistics. In this study, we examine a non- Archimedean copula from the Plackett family that is founded on the theory of constant cross product ratio. It is found that the Plackett family not only performs well at the bivariate level, but also allows a hierarchical multivariate stochastic analysis where the lower-level dependencies between variables can be fully preserved. The feasible range of Plackett parameters that would result in valid (compatible) 3-copulas is determined numerically. This trivariate Plackett family of copulas is then applied to construct the design rainfall hyetograph for several stations in Indiana where the estimated parameters lie in the feasible region. Based on a given design rainfall depth and duration, conditional expectations of rainfall features such as expected peak intensity, time to peak, and percentage cumulative rainfall at 10% cumulative time increments are estimated. The results of this study suggest that the constant cross product ratio theory can be extended to continuous random variables, and that it provides further flexibility for multivariate stochastic analyses of rainfall.
H33A-0965
A copula-based method to fill in missing data for daily rainfall
In this article, we describe and test a method to fill in missing values in daily rainfall datasets. This method is based on a copula-based bivariate models. Copulae are functions that are commonly used in statistics to approximate multivariate distributions. We describe how to infere the parameters of this model using historical data and validate it. Then, for a given day, this probabilistic model is used to estimate the probability of rainfall event at a rain gage station given another one and the expected value of rainfall amount. These quantities are then integrated by a logistic regression for the probabilities and a linear regression for the expected amounts in order to get a final estimate of the missing value of rainfall. This model is tested against commonly used methods, such as direct linear regression or ordinary kriging on a dataset of 43 rain gage station from Florida. Cross-validation shows that this model provides a good estimate of missing values, with a significant departure from linear models for heavy rainfall events.
H33A-0966
Geometric Modeling of Rainfall Distributions
A deterministic geometric procedure resulting in a wide range of complex patterns over one and two dimensions, as transformations of multifractal meassures via fractal functions, is explained. It is shown that such notions may be used to generate distributions that closely resemble observed rainfall distributions over one and two dimensions in a manner that does not require stochastic methods. The ideas are illustrated by showing suitable evolutions of generated rainfall sets, as their geometric parameters are varied. The implications of the results are also discussed.
H33A-0967
The remarkable wide range spatial scaling of TRMM precipitation
The advent of space borne precipitation radar has opened up the possibility of studying the variability of global precipitation over huge ranges of scale while avoiding many of the calibration and sparse network problems which plague ground based rain gage and radar networks. We studied 1176 consecutive orbits of attenuation- corrected near surface reflectivity measurements from the TRMM satellite PR instrument. We find that for well- measured statistical moments (orders 0 < q < 2) corresponding to dBZ < 57 and probabilities > 10**-6, that the residuals with respect to a pure scaling (power law) variability are remarkably low: to within 6.4 percent over the range 20,000 km down to 4.3 km. We argue that higher order moments are biased due to inadequately corrected attenuation effects. When a stochastic three - parameter universal multifractal cascade model is used to model both the reflectivity and the minimum detectable signal of the radar (which was about twice the mean), we find that we can explain all the same statistics to within 4.6 percent over the same range. The effective outer scale of the variability was found to be 32,000 +- 2000 km. The fact that this is somewhat larger than the planetary scale (20,000 km) is a consequence of the residual variability of precipitation at the planetary scales. With the help of numerical simulations we were able to estimate the three fundamental parameters as alpha = 1.5, C1 = 0.63 +- 0.02 and H = 0.00 +- 0.01 (the multifractal index, the codimension of the mean and the nonconservation parameter respectively). There was no error estimate on α since although alpha = 1.5 was roughly the optimum value, this conclusion depended on assumptions about the instrument at both low and high reflectivities. The value H = 0 means that the reflectivity can be modeled as a pure multiplicative process, i.e. that the reflectivity is conserved from scale to scale. We show that by extending the model down to the inner "relaxation scale" where the turbulence and rain decouple (in light rain, typically about 40 cm), that even without an explicit threshold, the model gives quite reasonable predictions about the frequency of occurrence of perceptible precipitation rates. While our basic findings (the scaling, outer scale) are almost exactly as predicted twenty years on the basis on ground based radar and the theory of anisotropic (stratified) cascades, they are incompatible with classical turbulence approaches which require at least two isotropic turbulence regimes. They are also incompatible with classical meteorological phenomenology which identifies morphology with mechanism and breaks up the observed range 4 km - 20 000km into several subranges each dominated by different mechanisms. Finally, since the model specifies the variability over huge ranges, it shows promise for resolving long standing problems in rain measurement from both (typically sparse) rain gage networks and radars.
H33A-0968
Stochastic generation of precipitation ensembles using remotely sensed information.
Realistic rainfall ensembles are crucial for hydrologic applications of ensemble predictions and data assimilation. In particular, ensemble prediction and assimilation algorithms can be expected to work better when the random precipitation events used to derive sample covariances or to force the land surface models have a spatio-temporal structure similar to observed rainfall. In this paper we present a procedure for generating rainfall replicates from on hourly GOES cloud top temperature data and space-time statistics derived from NOWRAD radar data. The first step in this procedure uses the GOES data to determine the size and shape of rainfall clusters. The second step simulates mutliple realizations of rainfall within these clusters. The number of rainfall peaks (local maxima of rain intensity) within a particular cluster is determined from the cluster size. The locations and intensities of these peaks are generated randomly using probabilistic descriptors derived from NOWRAD images. The algorithm's ability to generate replicates that are statistically similar to observations is verified using a multiattribute rank histogram analysis. The method is illustrated with an example that covers the United States Great Plains (at 0.5 degree spatial resolution) during the summer of 2004.
H33A-0969 [WITHDRAWN]
A Comparison Between NEXRAD and Rain Gage Interpolation in the Semi-Arid Climate of South Central Texas
The forcing data required for a simple hydrologic model are precipitation and evaporation. Traditionally, weather data is acquired from single point gauges and applied using Thiessen polygons over the modeled area. This technique is standard practice, and adequate in a climate with significant frontal weather systems or in a densely gauged area. The Sandies and Elm watershed is located in rural south central Texas. This area is sparsely gauged and has a semiarid climate known for its significant convective storm events. The flow variability of the streams in the Sandies and Elm watershed is defined by these convective storm systems. The hydrologic model needed to be calibrated to these storm events, therefore the storm event data input into the model should accurately represent precipitation with reference to both volume and spatial distribution. Using Geographic Information Systems (GIS), a comparative study between a spatial interpretation of the rain gauge data and NEXRAD (NEXt generation RADar) data was undertaken. The most severe frontal and convective storms were studied for each of the twelve months using a data set from the years 2000 through 2004. The 24- hour precipitation value range and total precipitation were calculated. The 24-hour precipitation spatial images were created for both the rain gauge interpretation and NEXRAD. A comparison of these values and figures were made and verified against the concurrent stream gauge fluctuation. This comparison demonstrated the weakness in gauge interpolation in areas of significant convective storm events. Overall the rain gauges underestimated the precipitation measured by NEXRAD 70% of the time. When the total precipitation was underestimated it was underestimated by an average of 43.2%.
H33A-0970
Radar Image and Rain-gauge Alignment using the Multi-resolution Viscous Alignment (MVA) Algorithm
Rainfall is a complex environmental variable that is difficult to describe either deterministically or statistically. To understand rainfall behaviors, many types of instruments are employed to detect and collect rainfall information. Among them, radar seems to provide the most comprehensive rainfall measurement at fine spatial and temporal resolution and over a relatively wide area. Nevertheless, it does not detects surface rainfall directly like what rain-gauge does. The accuracy radar rainfall, therefore, depends greatly on the Z-R relationship which convert radar reflectivity (Z) to surface rainrate (R). This calibration is usually done by fitting the rain-gauge data with the corresponding radar reflectivity using the regression analysis. To best fit the data, the radar reflectivity at neighbor pixels are usually used to best match the rain-gauge data. However, when applying the Z-R relationship to the radar image, there is no position adjustment despite the calibration technique. Hence, it is desirable to adjust the position of the radar reflectivity images prior to applying the Z-R relationship to improve the accuracy of the rainfall estimation. In this research, the Multi-resolution Viscous Alignment (MVA) algorithm is applied to best align radar reflectivity images to rain-gauge data in order to improve rainfall estimation from the Z-R relationship. The MVA algorithm solves the motion estimation problems using a Bayesian formulation to minimize misfits between two data sets. In general, the problem are ill-posed; therefore, some regularizations and constraints based on smoothness and non-divergence assumptions are employed. This algorithm is superior to the conventional techniques and correlation based techniques. It is fast, robust, easy to implement, and does not require data training. In addition, it can handle higher-order, missing data, and small-scale deformations. The algorithm provides spatially dense, consistency, and smooth transition vector. The MVA algorithm is employed to align more than 30 pairs of radar and rain-gauge data during the 2005 rainy season in Bangkok. The results show that the rainfall estimates after the alignment with MVA algorithm is superior than those without the alignment. This concept will lead to more efficient use of all available rainfall data, provide more accurate estimation of spatial rainfall in Thailand, as well as improve the confidence of using radar images to represent surface rainfall in many region of the world.
H33A-0971
Local Heavy Rainfall In Northern Kyushu In Japan By Typhoon No.0613
In Japan, heavy rainfalls originate from "stationary front" or "typhoon". In particular, typhoon plays an important role in the enhancement of stationary front and, subsequently, the occurrence of heavy rainfalls due to the supply of ample moisture. Therefore, paying attention to the movement and location of typhoon No.0613 in 2006, this study investigates the features of heavy rainfalls that occurred in northern Kyushu located in the west of Japan. In this event, 20mm/hr or more rainfalls were recorded in all AMeDAS observation points and, consequently, more than ten persons were died and missing due to the landslide disaster. Three peaks of rainfalls were closely related to the location of the typhoon. The first and second peaks were 94mm/hr (0600 to 0700JST) and 91mm/hr (0900 to 1000JST), respectively. These peaks were caused by the enhancement of the stationary front by southern wind (containing ample water vapor) that originates from the typhoon No.0613, which was 2,000km or more, far away from northern Kyushu. On the other hand, the third peak, 72mm/hr (1500 to 1600 JST), was caused by the direct effect of typhoon No.0613, which landed at 1800JST around Sasebo in northern Kyushu. It is necessary to note "disastrous local heavy rainfalls occur, even if a typhoon is 2000km or more, far away from heavy rainfall area, under the influence of the stationary front."
H33A-0972
Improving Estimation of Over-Lake Precipitation - An Application to Lake Erie
Over-lake precipitation is a key component of the water balance of the Great Lakes. Its correct estimation is, therefore, vital for planning and operational purposes. Yet, reliable estimates of precipitation are difficult to obtain in the Great Lakes region not only due to the lack of gages over the lakes themselves, but also due to the scarcity of gages in the draining basins. Traditionally, over-lake precipitation has been estimated by distance-weighted or other data-driven interpolation methods. In spite of their wide acceptance, these conventional methods suffer from intrinsic limitations as they fail to take into account the spatial and temporal variability of rainfall. Recently, multisensor products combining radar-based precipitation estimates and rain gage data (MPE) have provided a suitable alternative to estimates based on the sparse gage data. However, the presence of biases in the MPE data has raised serious concerns about their accuracy. A promising approach for overcoming the limitations of either type of data for producing better precipitation estimates is to spatially integrate the MPE data with the gage observations in a geostatistical framework. Using available gage and MPE data for the Lake Erie region, we propose a suite of spatial interpolation techniques based on universal kriging, for estimating monthly-averaged over-lake precipitation. The estimates from these techniques are compared to (i) more traditional methods such as inverse-distance weighted interpolation and ordinary kriging, both of which use only the gage data and (ii) the available MPE data. Results indicate that the universal kriging setup outperforms the estimation methods based only on one of the two data types, by providing estimates with significantly lower root mean square error and lower overall bias. Overall, the results demonstrate the robustness of the proposed approach in assimilating information from two different data types for providing more accurate and reliable estimates of over-lake precipitation.
H33A-0973
Modeling Radar-Rainfall Estimation Uncertainties Using Parametric and Non-Parametric Approaches
There are large uncertainties associated with radar estimates of rainfall. These errors include both deterministic and random effects of several sources. The deterministic component can be described mathematically in terms of a conditional expectation function and is the focus of this study. Two different approaches will be presented and applied: non-parametric (kernel-based) and parametric (copula-based). A large sample (more than six years) of rain gauge measurements from a highly dense network located in south-west England (Brue catchment) is used as an approximation of the true ground rainfall. These data are complemented with rainfall estimates by a C-band weather radar (Wardon Hill) located at about 40 km from the catchment. The authors compare the results obtained using the above two approaches for four temporal scales of hydrologic interest (5- and 15-minute, hourly and three-hourly) by means of several different performance indexes, and discuss weaknesses and strengths of each approach.
H33A-0974
On the Propagation of Radar-rainfall Estimation Uncertainties Into the Simulation of Different Rainfall-runoff Processes
Recent advances in remote sensing of rainfall provide unprecedented opportunities for acquiring rainfall measurements with high spatial and temporal resolutions. In particular, the Next Generation Weather Radar (NEXRAD) system is a promising resource for improving the accuracy and reliability of hydrologic predictions and operational forecasting. However, rainfall estimates from radar measurements are subject to uncertainties caused by both instrumental effects and lack of unique relation between radar-rainfall estimations and the surface rainfall quantities. The effect of such uncertainties on the predictive ability of hydrologic models is an active area of research. This study will investigate the propagation of radar-rainfall estimation uncertainties into the simulation of different rainfall-runoff processes. The analysis is performed over a mid-size watershed that is heavily monitored by a dense network of rainfall and streamflow gauges. The study uses a physically-based distributed hydrological model (Gridded Surface Subsurface Hydrologic Analysis, GSSHA). The model will be calibrated and validated using several historical rainfall-runoff storms. Radar estimation errors will be first assessed in terms of their marginal error distribution and spatial and temporal auto-correlations. Then, radar- based runoff simulations will be assessed in comparison to simulations using data from the dense rain gauge network in the watershed. The study will examine the effect of radar-rainfall uncertainties on simulations of various processes such as infiltration, surface runoff, soil moisture, and streamflow. Then, a simulation-based stochastic model for the radar error will be developed based on its identified characteristics (i.e., marginal distribution and spatio-temporal correlations). This model will provide a tool for generating multiple realizations of the radar error field and enable examination of the probabilistic nature of the error propagation into runoff predictions.
H33A-0975
RADAR BASED PRECIPITATION FORECASTING FOR FLOOD WARNING
Precipitation is one of the most important inputs for flood warning. The accuracy of the measured precipitation controls the effectiveness of flood warning, while the forecasted precipitation increases the lead time of flood warning, this is vital for catastrophically flood warning as it provides time for flood management, such as the emergency evacuation of the people and properties within the flood prone area, so to avoid flood damages. This paper presents an algorithm for forecasting precipitation based on Chinese next generation weather radar- CINRAD for catastrophically flood warning. This algorithm includes radar data quality control, precipitation estimation and forecasting, result correction. The radar data, received at every 5-6 minutes, is quality controlled first to delete the data noises, the pre-processed radar data then is used to estimate the precipitation, which will be employed to calibrate the radar equation parameters, then the pre-processed radar data and calibrated radar equation parameters will be input to the precipitation procedure to forecast precipitation. A software based on the above algorithm is developed that can be used to forecast precipitation on real ˇ§Ctime. The radar in Guangzhou city, the biggest city in southern China is studied and the precipitation in 2005 and 2006 in Liuxihe River Basin in southern China were forecasted to validate the effectiveness, the results show this algorithm is encouraging and will be put into real-time operation in the flood warning of Liuxihe River in 2007.
H33A-0976
Analysis of TRMM and gauge rainfall in the La Plata River Basin in South America for hydrologic predictions
The accurate estimation of rainfall is crucial for flood and drought monitoring, hydroelectric generation, navigability of water bodies and water resources management. In developing regions of the world, available meteorological information is obtained from a coarse network of precipitation and streamflow gauges. In this context, satellite estimated precipitation constitutes an invaluable source of information to be used in the prediction of major flood events occurrence or in the estimation of seasonal to interannual streamflows. The La Plata River Basin, which is the second largest river basin in South America covering 3.2 x 106 km2, maintains one of the most densely populated regions in South America where natural fluctuations in precipitation and streamflows deeply affect the economic and social equilibrium of the region. Due to the heavy dependence of the emergent economies in the region on the water resources of the basin, it is necessary to quantify the biases of existent satellite products relative to gauge measurements in order to understand how errors in satellite-derived precipitation could affect simulated hydrological fluxes. Post-real time TRMM products (3B42 V.6), for the period 1998-2006, are contrasted to daily gridded precipitation available at 0.25 degree which have been generated with rain gauge information existing in the basin (Liebmann and Allured, 2005). Spatial and temporal maps of satellite errors were created as the difference between TRMM and observations. These maps are generated at different temporal scales of importance for hydrologic applications such as daily, pentad or decadal and for the four seasons. The spatial errors allow us to identify regions on the basin where satellite estimates over/underestimate precipitation amounts and intensities. Results of the study estimate the impact of error structure existent in precipitation estimates on the simulation of the hydrologic cycle and allow us to asses what is the potential value of satellite products for seasonal to interannual hydrologic prediction of runoff and for water resources management.
H33A-0977
Can we Use Satellite-Rainfall to Predict Floods in Small Mountainous Basins?
One of the main advantages of satellite precipitation remote sensing is their ability to provide information over remote areas such as complex terrain and tropical rainforests where few, or no, in-situ observations are available. This study focuses on a well-instrumented small-scale mountainous basin (~116 km2) in the Northeastern Italy aiming at i) evaluating two different satellite-rainfall products (TRMM 3B42 and CMORPH), through a comparison with rain gauge observations and ii) investigating whether rainfall retrievals from satellites can be utilized to predict flood occurrences in such complex terrain basins. The error of the satellite-rainfall estimates is statistically characterized and its propagation effect to the hydrologic prediction is evaluated by using a distributed hydrologic model to simulate the rainfall-runoff transformation and compare the results with discharge observations.
H33A-0978
Verification of Satellite Rainfall Estimates from the Tropical Rainfall Measuring Mission over Ground Validation Sites
The Tropical Rainfall Measuring Mission's (TRMM) Ground Validation (GV) Program was originally established with the principal long-term goal of determining the random errors and systematic biases stemming from the application of the TRMM rainfall algorithms. The GV Program has been structured around two validation strategies: 1) determining the quantitative accuracy of the integrated monthly rainfall products at GV regional sites over large areas of about 500 km2 using integrated ground measurements and 2) evaluating the instantaneous satellite and GV rain rate statistics at spatio-temporal scales compatible with the satellite sensor resolution (Simpson et al. 1988, Thiele 1988). The GV Program has continued to evolve since the launch of the TRMM satellite on November 27, 1997. This presentation will discuss current GV methods of validating TRMM operational rain products in conjunction with ongoing research. The challenge facing TRMM GV has been how to best utilize rain information from the GV system to infer the random and systematic error characteristics of the satellite rain estimates. A fundamental problem of validating space-borne rain estimates is that the true mean areal rainfall is an ideal, scale-dependent parameter that cannot be directly measured. Empirical validation uses ground-based rain estimates to determine the error characteristics of the satellite-inferred rain estimates, but ground estimates also incur measurement errors and contribute to the error covariance. Furthermore, sampling errors, associated with the discrete, discontinuous temporal sampling by the rain sensors aboard the TRMM satellite, become statistically entangled in the monthly estimates. Sampling errors complicate the task of linking biases in the rain retrievals to the physics of the satellite algorithms. The TRMM Satellite Validation Office (TSVO) has made key progress towards effective satellite validation. For disentangling the sampling and retrieval errors, TSVO has developed and applied a methodology that statistically separates the two error sources. Using TRMM monthly estimates and high-resolution radar and gauge data, this method has been used to estimate sampling and retrieval error budgets over GV sites. More recently, a multi- year data set of instantaneous rain rates from the TRMM microwave imager (TMI), the precipitation radar (PR), and the combined algorithm was spatio-temporally matched and inter-compared to GV radar rain rates collected during satellite overpasses of select GV sites at the scale of the TMI footprint. The analysis provided a more direct probe of the satellite rain algorithms using ground data as an empirical reference. TSVO has also made significant advances in radar quality control through the development of the Relative Calibration Adjustment (RCA) technique. The RCA is currently being used to provide a long-term record of radar calibration for the radar at Kwajalein, a strategically important GV site in the tropical Pacific. The RCA technique has revealed previously undetected alterations in the radar sensitivity due to engineering changes (e.g., system modifications, antenna offsets, alterations of the receiver, or the data processor), making possible the correction of the radar rainfall measurements and ensuring the integrity of nearly a decade of TRMM GV observations and resources.
H33A-0979
Comparison of precipitation datasets over the tropical South American and African Continents.
Six rainfall datasets are compared over the Amazon basin, the Northeast Brazil and the Congo basin. These datasets include three gauge-only precipitation products from the Climatic Prediction Center (CPC), Global Precipitation Climatology Center (GPCC) and Brazilian Weather Forecast and Climate Studies Center (CLMNLS), and three combined gauge and satellite precipitation datasets from the CPC Merged Analysis of Precipitation (CMAP), Global Precipitation Climatology Project (GPCP) precipitation, and Tropical Rainfall Measuring Mission (TRMM) product. The spatial pattern of the annual precipitation is consistently represented by these data, despite of the differences in methods and periods of averaging. Quantitatively, the differences in annual precipitation among these datasets are 3% over our Amazon domain (0-15S, 50-70W), 17% over the Northeast Brazil (5-10S, 35-45W) and 12% the Congo domain (5N-10S, 15-30E). However the seasonal differences were. Over the Amazon domain, the rainfall variations are well correlated between CPC, GPCC, TRMM, GPCP and GPCC (>0.9) except for the northwestern Amazon. Over the Congo basin, the correlation between these rainfall datasets is generally below 0.7. The Empirical Orthogonal Functions analysis suggests large discrepancies in interannual and decadal variations of rainfall among these datasets, especially for the Congo basin and for the South American region after 1998.