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Geostatistical Analysis of the Spatial Distribution Of GEOSTATISTICAL ANALYSIS OF THE SPATIAL DISTRIBUTION OF PRECIPITATION IN THE SAN FRANCISCO BAY AREA FROM 1890 TO 2013: A GIS APPROACH __________________ A University Thesis Presented to the Faculty of California State University, East Bay In Partial Fulfillment of the Requirements for the Degree Master of Arts in Geography __________________ By Patricia Ann Allred August, 2016 Abstract This study has modeled spatial distribution of precipitation in the San Francisco Bay Area using geostatistical analysis in a GIS to aid regional water resource managers and planners. The main objectives of this study were: (1) use geostatistical methods to estimate, analyze, model and characterize the spatial variability of precipitation over 124 years from 1890 to 2013 using measured and simulated rain gauge data, (2) interpolate 49 precipitation maps representing 5 climate time periods spanning 31 years within the 1890 to 2013 timeline. Precipitation data from a combination of 58 weather station rain gauges was collected across 10 counties surrounding the San Francisco Bay region. Geostatistical analysis provided a set of statistical tools for incorporating the spatial correlation of measured and simulated observations to interpolate a continuous rainfall surface. All maps showed a consistent trend of precipitation rain bands. Highest values were located in the northwest, gradually decreasing to the lowest precipitation values in the southeast section of the study area. Storms generated in the Pacific Ocean were shown to track primarily from the northwest to the southeast. Topographical influences of the coastal ranges and valley basins displayed orographic effects that were visually displayed by the spatial distribution of precipitation on all maps. Results of this study confirm other research using geostatistical techniques, that for low-density rain gauge networks, geostatistical interpolation is a feasible option for spatial representation of local and regional precipitation in the San Francisco Bay Area. ii GEOSTA TIS TICAL ANALYSIS OF THE SPATIAL DISTRIBUTION OF PRECIPITATION IN THE SAN FRANCISCO BAY AREA FROM 1890 TO 2013: A GIS APPROACH By Patricia Ann Allred Approved: Date: ~) David Woo, Ph.D. (Cha· ) ~Cf ~ · Gary Li, Ph.D. iii Acknowledgements I would like to thank my Committee Chair, Dr. David Woo whose guidance, feedback, patience and meticulous attention to detail have been invaluable to me. I would also like to thank Dr. David Larson who painstakingly edited every word to make sure this research thesis represented the highest standards of professional writing. I want to thank Dr. Gary Li for his knowledge of GIS and for pointing me in the right direction. I would like to thank my husband Devon, for his patience, support and constant encouragement. His steady belief in my journey has been unwavering. iv Table of Contents Abstract ....................................................................................................................... ii Acknowledgements .................................................................................................... iv List of Tables ............................................................................................................. vii List of Figures ............................................................................................................ ix List of Maps ............................................................................................................... xi Chapter 1 – Introduction ........................................................................................... 1 1.1 Introduction ............................................................................................................ 1 1.2 Statement of the Problem ....................................................................................... 5 1.3 Focus of the study ................................................................................................... 6 1.4 Purpose of the study ............................................................................................... 8 1.5 Scope of the study .................................................................................................. 9 1.6 Study Area ............................................................................................................ 10 1.7 Map elements........................................................................................................ 11 1.8 Understanding the climate of the San Francisco Bay Area .................................. 15 1.9 Summary............................................................................................................... 19 Chapter 2 Literary Review ...................................................................................... 21 Section 1 ..................................................................................................................... 21 2.1 Introduction .......................................................................................................... 21 2.1.1 Insufficient local water supplies and dependence on non-local water resources .................................................................................................. 21 2.1.2 Impact of changes in the climate ....................................................................... 25 2.1.3 Recommendations for new and expanded water storage facilities ................... 26 Section 2 ..................................................................................................................... 27 2.2 The value of modeling the spatial distribution of precipitation ............................ 27 2.2.1 Geostatistical analysis of precipitation .............................................................. 28 2.2.2 Data transformation ........................................................................................... 31 2.2.3 Differences in temporal measurement of precipitation ..................................... 34 2.2.4 Kriging and the semivariogram ......................................................................... 39 2.2.5 Comparisons between OK and SK .................................................................... 43 v 2.2.6 Comparisons of geostatistical interpolation methods ........................................ 45 2.2.7 Comparisons of univariate and multivariate analysis ........................................ 48 2.2.8 Cross validation ................................................................................................. 54 Chapter 3 – Methodology ........................................................................................ 58 3.1 Introduction .......................................................................................................... 58 3.1.1 Structure and parameters of the study ............................................................... 59 3.1.2 Data collection ................................................................................................... 59 3.2.1 Data processing ................................................................................................. 70 3.2.2 Exploring the data.............................................................................................. 75 3.2.3 Determining autocorrelation using the semivariogram ..................................... 78 3.2.4 Checking for data trends .................................................................................... 84 3.2.5 Trend Removal .................................................................................................. 85 3.3 Determination of model parameters ..................................................................... 86 3.3.1 Fitting the kriging model to the semivariogram ................................................ 91 3.3.2 Simple Kriging and Ordinary Kriging ............................................................... 92 3.3.3 Prediction standard error maps .......................................................................... 93 3.4 Model diagnostics ................................................................................................. 95 3.5 Raster maps .......................................................................................................... 99 3.5.1 Map descriptions and method of formation ..................................................... 100 3.5.2 Climate comparison maps ............................................................................... 102 Chapter 4 – Results and Analysis .......................................................................... 105 4.1 Spatial and temporal precipitation observations ................................................. 105 4.2 Cross-validation geostatistical results ................................................................ 105 4.3 Color and design of precipitation and spatial distribution .................................. 110 4.4 Analysis of monthly precipitation, climates 1-4, Maps 1-36 ............................. 120 4.5 Effects of topography on precipitation in the SFBA .......................................... 124 4.6 Analysis of climates 1-4, annual average precipitation, Maps 37-40 ................. 131 4.7 Analysis of Maps 41-45...................................................................................... 135 4.8 Results of precipitation differences between climates 1-4 with 5 ...................... 138 4.9 Rain bands .........................................................................................................
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