• Berezowski, T., M. Szczeniak, I. Kardel, R. Michalowski, T. Okruszko, A. Mezghani, and M. Piniewski, 2016: CPLFD-GDPT5: High-resolution gridded daily precipitation and temperature data set for two largest Polish river basins. Earth Syst. Sci. Data, 8, 127139, https://doi.org/10.5194/essd-8-127-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Biau, G., E. Zorita, H. Von Storch, and H. Wackernagel, 1999: Estimation of precipitation by kriging in the EOF space of the sea level pressure field. J. Climate, 12, 10701085, https://doi.org/10.1175/1520-0442(1999)012<1070:EOPBKI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bostan, P. A., G. B. M. Heuvelink, and S. Z. Akyurek, 2012: Comparison of regression and kriging techniques for mapping the average annual precipitation of Turkey. Int. J. Appl. Earth Obs. Geoinf., 19, 115126, https://doi.org/10.1016/j.jag.2012.04.010.

    • Search Google Scholar
    • Export Citation
  • Breiman, L., 2001: Random forests. Mach. Learn., 45, 532, https://doi.org/10.1023/A:1010933404324.

  • Brinckmann, S., S. Krähenmann, and P. Bissolli, 2016: High-resolution daily gridded data sets of air temperature and wind speed for Europe. Earth Syst. Sci. Data, 8, 491516, https://doi.org/10.5194/essd-8-491-2016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Buytaert, W., R. Celleri, P. Willems, B. De Bièvre, and G. Wyseure, 2006: Spatial and temporal rainfall variability in mountainous areas: A case study from the south Ecuadorian Andes. J. Hydrol., 329, 413421, https://doi.org/10.1016/j.jhydrol.2006.02.031.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statistical-topographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140158, https://doi.org/10.1175/1520-0450(1994)033<0140:ASTMFM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dawdy, D. R., and W. B. Langbein, 1960: Mapping mean areal precipitation. Int. Assoc. Sci. Hydrol. Bull., 5, 1623, https://doi.org/10.1080/02626666009493176.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Deutsch, A., and A. G. Journel, 1992: Geostatistical Software Library and User’s Guide. Oxford University Press, 340 pp.

  • Ekwaru, J. P., and P. J. Veugelers, 2018: The overlooked importance of constants added in log transformation of independent variables with zero values: A proposed approach for determining an optimal constant. Stat. Biopharm. Res., 10, 2629, https://doi.org/10.1080/19466315.2017.1369900.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frauendorf, T. C., R. A. MacKenzie, R. W. Tingley, A. G. Frazier, M. H. Riney, and R. W. El-Sabaawi, 2019: Evaluating ecosystem effects of climate change on tropical island streams using high spatial and temporal resolution sampling regimes. Global Change Biol., 25, 13441357, https://doi.org/10.1111/gcb.14584.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frazier, A. G., and T. W. Giambelluca, 2017: Spatial trend analysis of Hawaiian rainfall from 1920 to 2012. Int. J. Climatol., 37, 25222531, https://doi.org/10.1002/joc.4862.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frazier, A. G., T. W. Giambelluca, H. F. Diaz, and H. L. Needham, 2016: Comparison of geostatistical approaches to spatially interpolate month-year rainfall for the Hawaiian Islands. Int. J. Climatol., 36, 14591470, https://doi.org/10.1002/joc.4437.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Frazier, A. G., O. Elison Timm, T. W. Giambelluca, and H. F. Diaz, 2018: The influence of ENSO, PDO and PNA on secular rainfall variations in Hawai’i. Climate Dyn., 51, 21272140, https://doi.org/10.1007/s00382-017-4003-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giambelluca, T. W., Q. Chen, A. G. Frazier, J. P. Price, Y. L. Chen, P. S. Chu, J. K. Eischeid, and D. M. Delparte, 2013: Online rainfall atlas of Hawai’i. Bull. Amer. Meteor. Soc., 94, 312316, https://doi.org/10.1175/BAMS-D-11-00228.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Goovaerts, P., 2000: Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall. J. Hydrol., 228, 113129, https://doi.org/10.1016/S0022-1694(00)00144-X.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hattermann, F. F., M. Wattenbach, V. Krysanova, and F. Wechsung, 2005: Runoff simulations on the macroscale with the ecohydrological model SWIM in the Elbe catchment – Validation and uncertainty analysis. Hydrol. Processes, 19, 693714, https://doi.org/10.1002/hyp.5625.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hengl, T., G. B. M. Heuvelink, and D. G. Rossiter, 2007: About regression-kriging: From equations to case studies. Comput. Geosci., 33, 13011315, https://doi.org/10.1016/j.cageo.2007.05.001.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hiemstra, P., 2015: Package “automap.” R package version 1.0-14, 15 pp., https://cran.r-project.org/web/packages/automap/automap.pdf.

    • Search Google Scholar
    • Export Citation
  • Jeffrey, S. J., J. O. Carter, K. B. Moodie, and A. R. Beswick, 2001: Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environ. Modell. Software, 16, 309330, https://doi.org/10.1016/S1364-8152(01)00008-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kitanidis, P. K., 1997: Introduction to Geostatistics. Cambridge University Press, 36 pp.

  • Krushelnycky, P. D., F. Starr, K. Starr, R. J. Longman, A. G. Frazier, L. L. Loope, and T. W. Giambelluca, 2016: Change in trade wind inversion frequency implicated in the decline of an alpine plant. Climate Change Responses, 3, 1, https://doi.org/10.1186/s40665-016-0015-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longman, R. J., and Coauthors, 2018: Compilation of climate data from heterogeneous networks across the Hawaiian Islands. Sci. Data, 5, 180012, https://doi.org/10.1038/sdata.2018.12.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longman, R. J., and Coauthors, 2019: High-resolution gridded daily rainfall and temperature for the Hawaiian Islands (1990–2014). J. Hydrometeor., 20, 489508, https://doi.org/10.1175/JHM-D-18-0112.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longman, R. J., A. J. Newman, T. W. Giambelluca, and M. Lucas, 2020: Characterizing the uncertainty and assessing the value of gap-filled daily rainfall data in Hawaii. J. Appl. Meteor. Climatol., 59, 12611276, https://doi.org/10.1175/JAMC-D-20-0007.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Longman, R. J., O. E. Timm, T. W. Giambelluca, and L. Kaiser, 2021: A 20-year analysis of disturbance-driven rainfall on O‘ahu, Hawai‘i. Mon. Wea. Rev., 149, 17671783, https://doi.org/10.1175/MWR-D-20-0287.1.

    • Search Google Scholar
    • Export Citation
  • Lucas, M. P., C. Trauernicht, A. G. Frazier, and T. Miura, 2020: Long-term, gridded standardized precipitation index for Hawai‘i. Data, 5, 109, https://doi.org/10.3390/data5040109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lucas, M. P., R. J. Longman, T. W. Giambelluca, A. G. Frazier, J. Mclean, S. B. Cleveland, Y. Haung, and J. Lee, 2021: Hawaii 1990–2019 gridded monthly rainfall mm. Hydroshare, accessed 5 December 2021, https://doi.org/10.4211/hs.2275657d62794c2294553919fa94b68d.

    • Search Google Scholar
    • Export Citation
  • Mair, A., and A. Fares, 2011: Comparison of rainfall interpolation methods in a mountainous region of a tropical island. J. Hydrol., 16, 371383, https://doi.org/10.1061/(ASCE)HE.1943-5584.0000330.

    • Search Google Scholar
    • Export Citation
  • Mair, A., A. G. Johnson, K. Rotzoll, and D. S. Oki, 2019: Estimated groundwater recharge from a water-budget model incorporating selected climate projections, Island of Maui, Hawai’i. Scientific Investigations Rep. 2019-5064, 46 pp., https://doi.org/10.3133/sir20195064.

    • Search Google Scholar
    • Export Citation
  • McLean, J. H., S. B. Cleveland, M. P. Lucas, R. J. Longman, T. W. Giambelluca, J. Leigh, and G. A. Jacobs, 2020: The Hawai‘i Rainfall Analysis and Mapping Application (HI-RAMA): Decision support and data visualization for statewide rainfall data. PEARC ′20: Practice and Experience in Advanced Research Computing, Portland, OR, SIGAPP/SIGHPC, 239245, https://doi.org/10.1145/3311790.3396668.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McLean, J. H., S. B. Cleveland, M. Dodge Ii, M. P. Lucas, R. J. Longman, T. W. Giambelluca, and G. A. Jacobs, 2022: Building a portal for climate data—Mapping automation, visualization, and dissemination. Concurrency Comput. Pract. Exp., https://doi.org/10.1002/cpe.6727, in press.

    • Search Google Scholar
    • Export Citation
  • Moral, F. J., 2010: Comparison of different geostatistical approaches to map climate variables: Application to precipitation. Int. J. Climatol., 30, 620631, https://doi.org/10.1002/joc.1913.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • New, M., M. Hulme, and P. Jones, 2000: Representing twentieth-century space-time climate variability. Part II: Development of 1901–96 monthly grids of terrestrial surface climate. J. Climate, 13, 22172238, https://doi.org/10.1175/1520-0442(2000)013<2217:RTCSTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Newman, A. J., M. P. Clark, R. J. Longman, and T. W. Giambelluca, 2019a: Methodological intercomparisons of station-based gridded meteorological products: Utility, limitations, and paths forward. J. Hydrometeor., 20, 531547, https://doi.org/10.1175/JHM-D-18-0114.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Newman, A. J., M. P. Clark, R. J. Longman, E. Gilleland, T. W. Giambelluca, and J. R. Arnold, 2019b: Use of daily station observations to produce high-resolution gridded probabilistic precipitation and temperature time series for the Hawaiian Islands. J. Hydrometeor., 20, 509529, https://doi.org/10.1175/JHM-D-18-0113.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nugent, A. D., R. J. Longman, C. Trauernicht, M. P. Lucas, H. F. Diaz, and T. W. Giambelluca, 2020: Fire and rain: The legacy of hurricane lane in Hawai‘i. Bull. Amer. Meteor. Soc., 101, E954E967, https://doi.org/10.1175/BAMS-D-19-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • R Core Team, 2018: R: A language and environment for statistical computing. R Foundation for Statistical Computing, https://www.R-project.org/.

    • Search Google Scholar
    • Export Citation
  • Stein, M. L., 1999: Interpolation of Spatial Data: Some Theory for Kriging. Springer, 93 pp.

  • Stewart, C. A., and Coauthors, 2015: Jetstream: A self-provisioned, scalable science and engineering cloud environment. Proc. of the 2015 XSEDE Conf.: Scientific Advancements Enabled by Enhanced Cyberinfrastructure, St. Louis, MO, XSEDE, 29, https://doi.org/10.1145/2792745.2792774.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tarboton, D. G., and Coauthors, 2014: HydroShare: Advancing collaboration through hydrologic data and model sharing. Seventh Int. Congress on Environmental Modelling and Software, San Diego, CA, International Environmental Modelling and Software Society, 29 pp., https://scholarsarchive.byu.edu/iemssconference.

    • Search Google Scholar
    • Export Citation
  • Towns, J., and Coauthors, 2014: XSEDE: Accelerating scientific discovery. Comput. Sci. Eng., 16, 6274, https://doi.org/10.1109/MCSE.2014.80.

  • Webster, R., and M. A. Oliver, 2001: Geostatistics for environmental scientists. Statistics in Practice, 2nd ed. John Wiley & Sons, 300 pp.

    • Search Google Scholar
    • Export Citation
  • Willmott, C. J., and S. M. Robeson, 1995: Climatologically aided interpolation (CAI) of terrestrial air temperature. Int. J. Climatol., 15, 221229, https://doi.org/10.1002/joc.3370150207.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Optimizing Automated Kriging to Improve Spatial Interpolation of Monthly Rainfall over Complex Terrain

Matthew P. LucasaWater Resource Research Center, University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Ryan J. LongmanaWater Resource Research Center, University of Hawai‘i at Mānoa, Honolulu, Hawaii
bEast-West Center, Honolulu, Hawaii

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Thomas W. GiambellucaaWater Resource Research Center, University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Abby G. FraziercGraduate School of Geography, Clark University, Worcester, Massachusetts

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Jared McleandInformation and Technology Services, Honolulu, Hawaii

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Sean B. ClevelanddInformation and Technology Services, Honolulu, Hawaii

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Yu-Fen HuangeDepartment of Natural Resources and Environmental Management, University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Jonghyun LeeaWater Resource Research Center, University of Hawai‘i at Mānoa, Honolulu, Hawaii
fDepartment of Civil Environmental Engineering, University of Hawai‘i at Mānoa, Honolulu, Hawaii

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Abstract

Gridded monthly rainfall estimates can be used for a number of research applications, including hydrologic modeling and weather forecasting. Automated interpolation algorithms, such as the “autoKrige” function in R, can produce gridded rainfall estimates that validate well but produce unrealistic spatial patterns. In this work, an optimized geostatistical kriging approach is used to interpolate relative rainfall anomalies, which are then combined with long-term means to develop the gridded estimates. The optimization consists of the following: 1) determining the most appropriate offset (constant) to use when log-transforming data; 2) eliminating poor quality data prior to interpolation; 3) detecting erroneous maps using a machine learning algorithm; and 4) selecting the most appropriate parameterization scheme for fitting the model used in the interpolation. Results of this effort include a 30-yr (1990–2019), high-resolution (250-m) gridded monthly rainfall time series for the state of Hawai‘i. Leave-one-out cross validation (LOOCV) is performed using an extensive network of 622 observation stations. LOOCV results are in good agreement with observations (R2 = 0.78; MAE = 55 mm month−1; 1.4%); however, predictions can underestimate high rainfall observations (bias = 34 mm month−1; −1%) due to a well-known smoothing effect that occurs with kriging. This research highlights the fact that validation statistics should not be the sole source of error assessment and that default parameterizations for automated interpolation may need to be modified to produce realistic gridded rainfall surfaces. Data products can be accessed through the Hawai‘i Data Climate Portal (HCDP; http://www.hawaii.edu/climate-data-portal).

Significance Statement

A new method is developed to map rainfall in Hawai‘i using an optimized geostatistical kriging approach. A machine learning technique is used to detect erroneous rainfall maps and several conditions are implemented to select the optimal parameterization scheme for fitting the model used in the kriging interpolation. A key finding is that optimization of the interpolation approach is necessary because maps may validate well but have unrealistic spatial patterns. This approach demonstrates how, with a moderate amount of data, a low-level machine learning algorithm can be trained to evaluate and classify an unrealistic map output.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ryan Longman, rlongman@hawaii.edu

Abstract

Gridded monthly rainfall estimates can be used for a number of research applications, including hydrologic modeling and weather forecasting. Automated interpolation algorithms, such as the “autoKrige” function in R, can produce gridded rainfall estimates that validate well but produce unrealistic spatial patterns. In this work, an optimized geostatistical kriging approach is used to interpolate relative rainfall anomalies, which are then combined with long-term means to develop the gridded estimates. The optimization consists of the following: 1) determining the most appropriate offset (constant) to use when log-transforming data; 2) eliminating poor quality data prior to interpolation; 3) detecting erroneous maps using a machine learning algorithm; and 4) selecting the most appropriate parameterization scheme for fitting the model used in the interpolation. Results of this effort include a 30-yr (1990–2019), high-resolution (250-m) gridded monthly rainfall time series for the state of Hawai‘i. Leave-one-out cross validation (LOOCV) is performed using an extensive network of 622 observation stations. LOOCV results are in good agreement with observations (R2 = 0.78; MAE = 55 mm month−1; 1.4%); however, predictions can underestimate high rainfall observations (bias = 34 mm month−1; −1%) due to a well-known smoothing effect that occurs with kriging. This research highlights the fact that validation statistics should not be the sole source of error assessment and that default parameterizations for automated interpolation may need to be modified to produce realistic gridded rainfall surfaces. Data products can be accessed through the Hawai‘i Data Climate Portal (HCDP; http://www.hawaii.edu/climate-data-portal).

Significance Statement

A new method is developed to map rainfall in Hawai‘i using an optimized geostatistical kriging approach. A machine learning technique is used to detect erroneous rainfall maps and several conditions are implemented to select the optimal parameterization scheme for fitting the model used in the kriging interpolation. A key finding is that optimization of the interpolation approach is necessary because maps may validate well but have unrealistic spatial patterns. This approach demonstrates how, with a moderate amount of data, a low-level machine learning algorithm can be trained to evaluate and classify an unrealistic map output.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ryan Longman, rlongman@hawaii.edu

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