Constraining Rainfall Replicates on Remote Sensed and In-Situ Measurements

Transcription

1 Constraining Rainfall Replicates on Remote Sensed and In-Situ Measurements Seyed Hamed Alemohammad, Dara Entekhabi, Dennis McLaughlin Ralph M. Parsons Laboratory for Environmental Science and Engineering Massachusetts Institute of Technology 92 nd American Meteorological Society Annual Meeting 22 nd - 26 th Jan New Orleans, LA

2 Motivation Availability of satellite-derived retrievals of rainfall; Full global coverage when compared to surface gauges; No reasonable assessment of the uncertainties associated with merged retrievals; An elegant way to express these uncertainties is to generate a realistic ensemble of rainfall replicates that each replicate of that is consistent with the original satellite observation while containing a random element. 2

3 Snapshots of Spatial Distribution of Rainfall Errors 3

4 PDF of Different Rainfall Measurements (numbers in brackets are probability of no rain) Data from Summer 2004 over US Great Plain. 4

5 Why Ensembles? Ensembles are useful for: propagating the uncertainty in hydrological and meteorological models (especially those used in data assimilation); probabilistic bili flash flood forecasting and risk analysis; used as a random forcing in a land surface model to derive probability distributions for all major surface hydrological variables;... Moreover, the derived distribution (approximated by Ensembles) constitute a prior that can be updated with measurements in data assimilation. 5

6 Objective In this study we propose a stochastic method to produce an ensemble of rainfall storms that can be constrained on satellite measurements and/or point measurements. 6

7 Methodology This method is based on joint statistics of sub-band coefficients of the rainfall measurement. The subbands are produced by filtering the original rainfall measurement using Steerable filters. 7

8 Steerable Filters Steerable filters (or equivalently Steerable pyramid) is a linear multi-scale, multi- orientation and self-inverting image decomposition. Structure of the Steerable pyramids in frequency domain (soruce: Liu et al.) 8

9 Steerable Image Transform (a) Original image (b) Steerable bandpass coefficients in a multiscale pyramid representation (a) (b) 9

10 Steerable Image Transform Original Rainfall Measurement Co oarser res solution subbands 10

11 Replicate Generation Steps The method has 2 steps: Scanning the Training Image (TI) and calculating the values of constraints; Generating a randomized rainfall and applying the constraints to that. In each of the two steps the corresponding TI or replicate is decomposed to several sub-bands bands using steerable pyramid. It s an iterative algorithm. 11

12 Constraints Histogram of Intensities. For the pixel intensities: range, variance, skewness and kurtosis; For the lowpass images of pyramid: the skewness and kurtosis. LocalAutocorrelation. ti Decomposition is overcomplete; Local autocorrelation of the lowpass images are measured. Coefficients' Magnitude Correlation. Features in an image give rise to large coefficients in local spatial neighborhoods, as well as at adjacent scales and orientation. Cross-scale Phase Statistics. Distinguishing edges from lines in the TI. 12

13 Outputs of Different Iterations in Generating a Replicate 13

14 Areal Support Constraining Potential rainy areas from cloud-top temperature, measured by Geostationary satellite sensors. (a) (b) (c) (a) Gaussian noise generated input (b) Cloud support (red areas are considered cloudy and blue ones not cloudy.) (c) Constrained input for the replicate generation method. 14

15 Results: No Constraints 15

16 Results: Areal Constraints 16

17 Results: Areal and Point Constraints 17

18 Evaluations No single metric can adequately measure the quality of an ensemble. So we have considered 3 metrics here: Histogram of cluster sizes distribution; CDF of rain rates; Jaccard distance, as a similarity index. 18

19 Evaluation: Histogram of Cluster Sizes Distribution Replicates with no Constraints Replicates with Areal Constraints 19

20 Evaluation: CDF of Rain Rates Gray color: Replicates Red color: TIs Replicates with no Constraints 20

21 Evaluation: CDF of Rain Rates Gray color: Replicates Red color: TIs Replicates with Areal Constraints 21

22 Evaluation: Jaccard Distance J = 1 f 01 + f f f 11 Green colors are the unconstrained replicates Blue colors are the replicates with areal support constraining Red colors are the replicates with Areal and point constraining 22

23 Conclusions The results proved the capability of this method in generating realistic rainfall replicates that are statistically similar to their corresponding TI. Moreover, the constraining option improves the replicates' spatial distribution and structure. The method has several parameters that can be changed to generate the desired degree of diversityi in the replicates according to their application. 23

24 Thanks for you attention. Questions?