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- Author or Editor: Mark Morrissey x
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Abstract
The effect of data resolution on the area threshold method is studied using a stochastic model of radar snapshots of tropical rainfall taken during the Global Atmospheric Research Program Atlantic Tropical Experiment. The results indicate that significant biases and random error can arise when using radar or satellite data having spatial resolutions different from those used to calibrate the area threshold method. Although the use of a threshold decreases the bias and random error in the fractional coverage of rain rates, the larger calibration coefficients associated with larger thresholds tend to increase the bias and random error in the resulting areal mean rain-rate estimates.
Abstract
The effect of data resolution on the area threshold method is studied using a stochastic model of radar snapshots of tropical rainfall taken during the Global Atmospheric Research Program Atlantic Tropical Experiment. The results indicate that significant biases and random error can arise when using radar or satellite data having spatial resolutions different from those used to calibrate the area threshold method. Although the use of a threshold decreases the bias and random error in the fractional coverage of rain rates, the larger calibration coefficients associated with larger thresholds tend to increase the bias and random error in the resulting areal mean rain-rate estimates.
Abstract
Satellite rainfall estimates from a microwave emission-based algorithm by Wilheit et al. are verified using the noncontiguous rain gauge method incorporating monthly Pacific atoll rain gauge data. The results are compared with those obtained using an infrared-based satellite algorithm, the GOES precipitation index. Comparisons between satellite estimates with simple Spatial averages of point rain gauge data are shown to be ineffective at identifying statistically significant differences between the two algorithms due to substantial amounts of spatial sampling error in the rain gauge spatial averages. By effectively reducing this error, the noncontiguous rain gauge method reveals distinctive differences in the ability of each of the algorithms to accurately estimate monthly rainfall over the open ocean. The results indicate that the microwave algorithm, while slightly biased, is significantly less biased than the infrared, which tends to overestimate high rainfall values and underestimate low rainfall values. However, the random error associated with both algorithms is essentially the same.
Abstract
Satellite rainfall estimates from a microwave emission-based algorithm by Wilheit et al. are verified using the noncontiguous rain gauge method incorporating monthly Pacific atoll rain gauge data. The results are compared with those obtained using an infrared-based satellite algorithm, the GOES precipitation index. Comparisons between satellite estimates with simple Spatial averages of point rain gauge data are shown to be ineffective at identifying statistically significant differences between the two algorithms due to substantial amounts of spatial sampling error in the rain gauge spatial averages. By effectively reducing this error, the noncontiguous rain gauge method reveals distinctive differences in the ability of each of the algorithms to accurately estimate monthly rainfall over the open ocean. The results indicate that the microwave algorithm, while slightly biased, is significantly less biased than the infrared, which tends to overestimate high rainfall values and underestimate low rainfall values. However, the random error associated with both algorithms is essentially the same.
Abstract
The effect of temporal sampling error in satellite estimates of climate-scale rainfall is to produce a “conditional” bias where the algorithm overestimates high rainfall and underestimates low rainfall. Thus, the bias is conditional on the value of the estimate. This paper illustrates the problem using satellite infrared rainfall estimates together with a well-known satellite algorithm and shows it to be a function of the averaging scale, the sampling rate, and the temporal autocorrelation structure of the satellite estimates. Using realistic sampling rates, it is shown that significant biases exist in satellite rainfall estimates if polar-orbiting data are used in their construction. A simple correction for this bias based upon the estimated autocorrelation structure is given.
Abstract
The effect of temporal sampling error in satellite estimates of climate-scale rainfall is to produce a “conditional” bias where the algorithm overestimates high rainfall and underestimates low rainfall. Thus, the bias is conditional on the value of the estimate. This paper illustrates the problem using satellite infrared rainfall estimates together with a well-known satellite algorithm and shows it to be a function of the averaging scale, the sampling rate, and the temporal autocorrelation structure of the satellite estimates. Using realistic sampling rates, it is shown that significant biases exist in satellite rainfall estimates if polar-orbiting data are used in their construction. A simple correction for this bias based upon the estimated autocorrelation structure is given.
Abstract
The use of the two-parameter Weibull function as an estimator of the wind speed probability density function (PDF) is known to be problematic when a high accuracy of fit is required, such as in the computation of the wind power density function. Various types of nonparametric kernels can provide excellent fits to wind speed histograms but cannot provide tractable analytical expressions. Analytic expressions for the wind speed PDF are needed for many applications, particularly in the downscaling of model or satellite wind speed estimates to the regional or point scale. It is demonstrated that the judicious use of an expansion of orthogonal polynomials can produce more accurate estimates of the wind speed PDF than relatively simply parametric functions, such as the commonly used Weibull function. This study examines four such expansions applied to two different surface wind speed datasets in Oklahoma. The results indicate that the accuracy of fit of a given expansion is strongly related to how close the basis weight function in an expansion resembles the wind speed histogram. It is shown that this basis function, which is the first term in the expansion, acts as a first “best guess” to the true wind speed PDF and that the additional terms act to “adjust” the fit to converge on the true density function. The results indicate that appropriately chosen orthogonal polynomials can provide an excellent fit and are quite tractable.
Abstract
The use of the two-parameter Weibull function as an estimator of the wind speed probability density function (PDF) is known to be problematic when a high accuracy of fit is required, such as in the computation of the wind power density function. Various types of nonparametric kernels can provide excellent fits to wind speed histograms but cannot provide tractable analytical expressions. Analytic expressions for the wind speed PDF are needed for many applications, particularly in the downscaling of model or satellite wind speed estimates to the regional or point scale. It is demonstrated that the judicious use of an expansion of orthogonal polynomials can produce more accurate estimates of the wind speed PDF than relatively simply parametric functions, such as the commonly used Weibull function. This study examines four such expansions applied to two different surface wind speed datasets in Oklahoma. The results indicate that the accuracy of fit of a given expansion is strongly related to how close the basis weight function in an expansion resembles the wind speed histogram. It is shown that this basis function, which is the first term in the expansion, acts as a first “best guess” to the true wind speed PDF and that the additional terms act to “adjust” the fit to converge on the true density function. The results indicate that appropriately chosen orthogonal polynomials can provide an excellent fit and are quite tractable.
Abstract
Rainfall estimates for two simple satellite-based rainfall algorithms are verified over the tropical Pacific using a new method that incorporates sparsely distributed raingages. The resulting linear regression relationship between monthly areal rainfall and the highly reflective cloud index agrees with earlier results. However, the GOES precipitation index (GPI), which was calibrated using radar rainfall data obtained from the eastern tropical Atlantic, produces biased areas rainfall estimates over most of the tropical Pacific. However, its precision is greater than the highly reflective cloud index, perhaps due to the GPI's larger spatial dimensions. With the incorporation of calibration coefficients determined in this study, the GPI will produce unbiased estimates of areal rainfall for the tropical Pacific region.
Abstract
Rainfall estimates for two simple satellite-based rainfall algorithms are verified over the tropical Pacific using a new method that incorporates sparsely distributed raingages. The resulting linear regression relationship between monthly areal rainfall and the highly reflective cloud index agrees with earlier results. However, the GOES precipitation index (GPI), which was calibrated using radar rainfall data obtained from the eastern tropical Atlantic, produces biased areas rainfall estimates over most of the tropical Pacific. However, its precision is greater than the highly reflective cloud index, perhaps due to the GPI's larger spatial dimensions. With the incorporation of calibration coefficients determined in this study, the GPI will produce unbiased estimates of areal rainfall for the tropical Pacific region.
Abstract
Multivariate statistical analyses are employed to identify the source areas of the fine particulates and sulfate, which are the primary components of summer haze in the Blue Ridge Mountains of Virginia. These analyses include principal component analysis followed by stepwise multiple regression analysis. The results indicate that most of the fine particles and sulfates originate in the Midwest. The most important factor for both parameters is the residence time of the air parcels over the Midwest. The results also indicate that the sulfate is formed by photochemically initiated reactions. Production of organic aerosols from natural hydrocarbon emissions is also identified as a minor source of fine particles in the Blue Ridge Mountains area.
Abstract
Multivariate statistical analyses are employed to identify the source areas of the fine particulates and sulfate, which are the primary components of summer haze in the Blue Ridge Mountains of Virginia. These analyses include principal component analysis followed by stepwise multiple regression analysis. The results indicate that most of the fine particles and sulfates originate in the Midwest. The most important factor for both parameters is the residence time of the air parcels over the Midwest. The results also indicate that the sulfate is formed by photochemically initiated reactions. Production of organic aerosols from natural hydrocarbon emissions is also identified as a minor source of fine particles in the Blue Ridge Mountains area.
Abstract
The relationship between the fractional time raining and tropical rainfall amount is investigated using raingage data and a point process model of tropical rainfall. Both the strength and the nature of the relationship are dependent upon the resolution of the data used to estimate the fractional time raining. It is found that highly accurate estimates of rainfall amounts over periods of one month or greater can be obtained from the fractional time raining so long as high-time-resolution data are used. It is demonstrated that the relationship between the fractional time raining and monthly atoll rainfall is quasi-homogeneous within the monsoon trough region of the equatorial western Pacific.
Abstract
The relationship between the fractional time raining and tropical rainfall amount is investigated using raingage data and a point process model of tropical rainfall. Both the strength and the nature of the relationship are dependent upon the resolution of the data used to estimate the fractional time raining. It is found that highly accurate estimates of rainfall amounts over periods of one month or greater can be obtained from the fractional time raining so long as high-time-resolution data are used. It is demonstrated that the relationship between the fractional time raining and monthly atoll rainfall is quasi-homogeneous within the monsoon trough region of the equatorial western Pacific.
Abstract
The goal of this study is to improve understanding of the optimization criteria for radar rainfall (RR) products. Conditional bias (CB) is formally defined and discussed. The CB is defined as the difference between a given rain rate and the conditional average of its estimates. A simple analytical model is used to study the behavior of CB and its effect on the relationship between the estimates and the truth. This study shows the measurement errors of near-surface radar reflectivity and the natural reflectivity–rainfall rate variability can affect CB. This RR estimation error component is also compared with the commonly used mean-square error (MSE). A dilemma between the minimization of these two errors is demonstrated. Removing CB from the estimates significantly increases MSE, but minimizing MSE results in a large CB that manifests itself in underestimation of strong rainfalls.
Abstract
The goal of this study is to improve understanding of the optimization criteria for radar rainfall (RR) products. Conditional bias (CB) is formally defined and discussed. The CB is defined as the difference between a given rain rate and the conditional average of its estimates. A simple analytical model is used to study the behavior of CB and its effect on the relationship between the estimates and the truth. This study shows the measurement errors of near-surface radar reflectivity and the natural reflectivity–rainfall rate variability can affect CB. This RR estimation error component is also compared with the commonly used mean-square error (MSE). A dilemma between the minimization of these two errors is demonstrated. Removing CB from the estimates significantly increases MSE, but minimizing MSE results in a large CB that manifests itself in underestimation of strong rainfalls.
Abstract
This study provides an intensive evaluation of the Global Precipitation Climatology Project (GPCP) 1° daily (1DD) rainfall products over the Mississippi River basin, which covers 435 1° latitude × 1° longitude grids for the period of January 1997–December 2000 using radar-based precipitation estimates. The authors’ evaluation criteria include unconditional continuous, conditional (quasi) continuous, and categorical statistics, and their analyses cover annual and seasonal time periods. The authors present spatial maps that reflect the results for the 1° grids and a summary of the results for three selected regions. They also develop a statistical framework that partitions the GPCP–radar difference statistics into GPCP error and radar error statistics. They further partition the GPCP error statistics into sampling error and retrieval error statistics and estimate the sampling error statistics using a data-based resampling experiment. Highlights of the results include the following: 1) the GPCP 1DD product captures the spatial and temporal variability of rainfall to a high degree, with more than 80% of the variance explained, 2) the GPCP 1DD product proficiently detects rainy days at a large range of rainfall thresholds, and 3) in comparison with radar-based estimates the GPCP 1DD product overestimates rainfall.
Abstract
This study provides an intensive evaluation of the Global Precipitation Climatology Project (GPCP) 1° daily (1DD) rainfall products over the Mississippi River basin, which covers 435 1° latitude × 1° longitude grids for the period of January 1997–December 2000 using radar-based precipitation estimates. The authors’ evaluation criteria include unconditional continuous, conditional (quasi) continuous, and categorical statistics, and their analyses cover annual and seasonal time periods. The authors present spatial maps that reflect the results for the 1° grids and a summary of the results for three selected regions. They also develop a statistical framework that partitions the GPCP–radar difference statistics into GPCP error and radar error statistics. They further partition the GPCP error statistics into sampling error and retrieval error statistics and estimate the sampling error statistics using a data-based resampling experiment. Highlights of the results include the following: 1) the GPCP 1DD product captures the spatial and temporal variability of rainfall to a high degree, with more than 80% of the variance explained, 2) the GPCP 1DD product proficiently detects rainy days at a large range of rainfall thresholds, and 3) in comparison with radar-based estimates the GPCP 1DD product overestimates rainfall.
Abstract
This paper focuses on estimating the error uncertainty of the monthly 2.5° × 2.5° rainfall products of the Global Precipitation Climatology Project (GPCP) using rain gauge observations. Two kinds of GPCP products are evaluated: the satellite-only (MS) product, and the satellite–gauge (SG) merged product. The error variance separation (EVS) method has been proposed previously as a means of estimating the error uncertainty of the GPCP products. In this paper, the accuracy of the EVS results is examined for a variety of gauge densities. Three validation sites—two in North Dakota and one in Thailand—all with a large number of rain gauges, were selected. The very high density of the selected sites justifies the assumption that the errors are negligible if all gauges are used. Monte Carlo simulation studies were performed to evaluate sampling uncertainty for selected rain gauge network densities. Results are presented in terms of EVS error uncertainty normalized by the true error uncertainty. These results show that the accuracy of the EVS error uncertainty estimates for the SG product differs from that of the MS product. The key factors that affect the errors of the EVS results, such as the gauge density, the gauge network, and the sample size, have been identified and their influence has been quantified. One major finding of this study is that 8–10 gauges, at the 2.5° scale, are required as a minimum to get good error uncertainty estimates for the SG products from the EVS method. For eight or more gauges, the normalized error uncertainty is about 0.86 ± 0.10 (North Dakota: Box 1) and 0.95 ± 0.10 (North Dakota: Box 2). Results show that, despite its error, the EVS method performs better than the root-mean-square error (rmse) approach that ignores the rain gauge sampling error. For the MS products, both the EVS method and the rmse approach give negligible bias. As expected, results show that the SG products give better rainfall estimates than the MS products, according to most of the criteria used.
Abstract
This paper focuses on estimating the error uncertainty of the monthly 2.5° × 2.5° rainfall products of the Global Precipitation Climatology Project (GPCP) using rain gauge observations. Two kinds of GPCP products are evaluated: the satellite-only (MS) product, and the satellite–gauge (SG) merged product. The error variance separation (EVS) method has been proposed previously as a means of estimating the error uncertainty of the GPCP products. In this paper, the accuracy of the EVS results is examined for a variety of gauge densities. Three validation sites—two in North Dakota and one in Thailand—all with a large number of rain gauges, were selected. The very high density of the selected sites justifies the assumption that the errors are negligible if all gauges are used. Monte Carlo simulation studies were performed to evaluate sampling uncertainty for selected rain gauge network densities. Results are presented in terms of EVS error uncertainty normalized by the true error uncertainty. These results show that the accuracy of the EVS error uncertainty estimates for the SG product differs from that of the MS product. The key factors that affect the errors of the EVS results, such as the gauge density, the gauge network, and the sample size, have been identified and their influence has been quantified. One major finding of this study is that 8–10 gauges, at the 2.5° scale, are required as a minimum to get good error uncertainty estimates for the SG products from the EVS method. For eight or more gauges, the normalized error uncertainty is about 0.86 ± 0.10 (North Dakota: Box 1) and 0.95 ± 0.10 (North Dakota: Box 2). Results show that, despite its error, the EVS method performs better than the root-mean-square error (rmse) approach that ignores the rain gauge sampling error. For the MS products, both the EVS method and the rmse approach give negligible bias. As expected, results show that the SG products give better rainfall estimates than the MS products, according to most of the criteria used.
