Analysis of the USGS Coastal Gradient Real-time Gaging Network

Transcription

1 Analysis of the USGS Coastal Gradient Real-time Gaging Network Paul Conrads, USGS, SC Water Science Center Kenneth Odom, USGS, CO Water Science Center Greater Everglades Ecosystem Restoration Conference July 13, 2010 U.S. Department of the Interior U.S. Geological Survey

2 USGS Coastal Gradient Network

3 Dataset Parameters: Stage, Salinity, Discharge, Temperature Hourly Data: ~36 Datasets Analyze uniqueness of information of each time series

4 Two Approaches Dynamic Time-series Clustering Groups time series with similar behaviors Cluster on R or R 2 of signal Principle Component Analysis (PCA) R l d ti i Re-sampled time series PCA on the resampled signals

5 Clustering Clustering is a geometry problem. Number of groups minimizes the distance of the group member to the mean of the group (k-means). Numerical score (RMSE) for the tightness of each group.

6 Dynamic Time-series Clustering Use Pearson coefficient (r) as the measure of the dynamic similarity il it between two sites. Build arrays of how sites relate dynamically between all the other sites. Use k-mean to cluster and determine optimal number of groups Di id d h Divide and conquer approach Big problem smaller problem

7 Simple Example 7 Water Level Sites How to objectively group stations with similar behavior?

8 Simple Example 7 Sites Cross correlation matrix produces arrays of Pearson coefficients for each station to the other stations. If all Pearson s are positive, use R 2 to magnify the differences between sites.

9 Example Cluster Results As the number of clusters increases, the RMSE error decreases. RMSE is the measure of the difference in distance RMSE is the measure of the difference in distance between each member and the mean of the group.

10 Group Assignments Group 1 Group 2 Group 3

11 Plots of Groups

12 Water-level Analysis 29 water-level time series used (five removed for short period of records Groups gages with similar behaviors Minimizes i i cumulative distances between each vector (the R 2 between two stations) and the mean of that vector s group Plot RMSE and number of groups 1 cluster has the highest RMSE 29 clusters has RMSE of zero

13 Breakout Curve Inflection point of the curve is at 7 clusters. Indicates that the optimal number of groups is 7. Can also be seen as point of diminishing returns for adding addition clusters.

14 Spatial Distribution of Water Level Clusters

15 Normalize Average Group Hydrographs Groups 1, 2, & 4 Groups 5 & 7 Groups 3 & 6

16 Group 1 Members Potential model R 2 > 0.87

17 Group 2 Members Potential models R 2 > 0.79

18 Group 3 Members Potential models R 2 >

19 Group 4 Members Potential models R 2 > 0.48

20 Group 5 Members Potential models R 2 >

21 Group 6 Members Potential models R 2 >

22 Group 7 Members Potential models R 2 > 0.81

23 Anomaly Eden 3 and Upstream Broad River Proximal gaging stations have very different Proximal gaging stations have very different hydrologic behaviors (river and marsh)

24 Ranking of Stations Pearson coefficient (r) () is a measure of shared information between two stations. The lower the r values (or R 2 ), the greater the uniqueness of the station information Ranked the stations within each group Groups with more than 4 stations: re- clustered to determine first sub-group of 1

25 Ranking of Small Groups

26 Ranking of Small Groups (con t)

27 Ranking of Group 2

28 Ranking of Group 2 (con t) Remove Barron and Lopez River from correlation matrix and re-cluster

29 Ranking of Group 7

30 PCA Groupings PCA Similar to dynamic clustering groups Dynamic

31 Detecting Hydrologic Change Approach sets up a baseline of behavioral relations between station. Repeat analysis in the future to see if there are changes in the baseline. Rankings could be used in a similar way. A change in rankings could be an indication of change. Both approaches could be applied in incremental steps with long-term datasets.

32 Summary Approach used on other parameters in the network Salinity Discharge Temperature Dynamic clustering good technique for objectively group time series with similar behaviors rank time series by uniqueness of information Determine system wide behavior changes

33 The End