A literature review of interpolated precipitation surfaces & implications for watershed modeling

1. A literature review of interpolated precipitation surfaces & implications for watershed modeling Julia Glenday 7 May 2010

2. Presentation outline • Background/Motivation • Methods to create precipitation surfaces • Impact of method on hydrologic model predictions • Conclusions/Ideas

3. Background/Motivation Goal: detect (and predict) the impact of land use and management on water supply from a 1,000 km2 watershed in South Africa • Regional precipitation gradients: average declining both moving inland and moving westward • Steep topographic gradients • Rainfall gauges along valley bottoms • What precipitation values to use in modeling? • Does hydrologic amplify or smooth out differences between methods of interpolation?

4. Interpolating from point data • Graphical– manually drawing isohyets from interpretation of topography, wind, etc. & analogous station data • Topographic– regressions with elevation, aspect, slope, wind direction, etc. • Numeric/statistical– using only the data and its spatial arrangement • Thiessen polygons • Inverse distance weighting (IDW) • Spline • Kriging • Combination/geostatistical • Detrended kriging, kriging with external drift • PRISM, Conditional interpolation Jansen, 2008 Govaaerts, 1999 http://www.cadtutor.net/tutorials/autocad/drawing_objects/draw-15.gif

5. Global level rainfall grid products • Coarse spatial scales (0.5o = 3,025 km2@ equator) • Monthly values • Validation done at global scales • Variety of methods to interpolate station data before summarizing to 0.5o: • Climate Research Unit (CRU) – thin plate splines implemented within longitude, latitude, and elevation ranges • Institut de Recherche pour le Développement (IRD) - SIEREM (Système d'Information Environnementale sur les Ressources en eaux et leur Modélisation) – kriging • Global PrecipitationClimatology Center (WMO) - kriging

7. Common problematic assumptions of interpolation methods (Hewitson & Crane 2005) • The precipitation field is continuous • The distance decay function of a station’s spatial representativeness is constant over time, seasons, etc. • Distance-decay is the same for all stations (IDW) • Distance-decay is constant in all radial directions (kriging) • Distance-decay is monotonic (vs. peak-valley-peak) • Influence of different surrounding stations on the estimate of a point are given the same weight (on top of a distance decay) if they are clustered together on one side of the point than if they were spread out around the point (IDW)

8. PRISM: Precipitation-elevation Regressions on Independent Slopes Model (Daly et al 1994, 2000) Process: • Use a DEM to group stations intotopographicfacets • Factetsbased on slope orientation – coarsenuntilreachthresholdnumber of stations per facet • Create and apply a localizedregression of precipitation vs elevation & or coastalproximity for a local radius within a facet • stations assigned to DEM elevations for regression: assume that fine scaletopography has lesseffectthanbroadscalefeatures Addresses: • Effects of elevation on precip • Spatial scale & pattern of orographiceffects Needshigh station density to improve on othermethods, doesn’taccount for other local factors of influence, or temporal variability in elevationrelationship

9. Conditional interpolation (Hewitson & Crane, 2005) Process: • Within a radius of targetcell use pattern of station values to derivesynopticatmospheric ‘states’ • using Self OrganizingMaps as a clusteringmethod • Use the pattern of wet/dry stations duringeachsynoptic ‘state’ to make a wet/dry probability surface (donesimilarly to Kriging) • Within areas predicted to bewet for the day’s state, interpolatefrom stations • Createthis surface at fine grid (0.1o), thencoarsenit Addresses: • Non continuity of precipitation – very important at the dailyscale • Distance-decayfunctions: state specific & states and the temporal pattern of states are determined by patterns in the data (ratherthanmakingmonthlyrelationships, etc) Needshigh station density to improve on othermethods, elevationimplicitlydealtonlygivenhigh station density

10. Method accuracy in practice • Test accuracy using cross validation at different scales (annual, seasonal means, extremes, dry vs. wet) • Methods show different comparative accuracy in different conditions: spatial scale of application & validation, topographic variability of region, seasonality • Output generally differs less between methods when there is high station density, simple terrain, coarser grids & temporal averaging • Low station low compared to topovar, output between methods will be more different, but the amount of error may be similar • Examples: • PRISM outperformed kriging when applied to Willamete Basin, all of the Western US (Daly 1994) • KED kriging outperformed ordinary krigingand IDW in complex terrain (Goovaerts 2000) • Many many methods over the whole EU: differences between methods at a given point is larger than the range of skill of a single method over space or season. Krigingperformed best on average over the region (Hofstra2008)

11. Implications for hydrologic modeling Depends on: • Size of watershed and density/distribution of gages • Variability of precipitation in space & time • Thresholds/sensitivity of processes, e.g. • infiltration rates & soil & groundwater storage capacity • landscape detention storage • vegetation drought tolerance • Output of interest, e.g. • Mean monthly streamflow • Cumulative streamflow over a time period (e.g. dam storage) • Extreme daily values (e.g. floods) • Model calibration compensation Ruelland et a l, 2008

12. Implicationsfor hydrologic modeling • Ruelland et al 2008: 13 stations, 100,000 km2 watershed, applied Thiessens, IDW, spline, & kriging - Hydrostrahler rainfall-runoff model • Cross validation: all low Nash Sutcliffe for daily precip (0.12), IDW & kriging more accurate (0.6-0.8) for 10-day • Watershed annual aveppt: spline highest (1179 mm), IDW lowest (1072 mm) – no way to validate • Daily streamflow: Nash-Sutcliffe work well for all in wet period (0.9), poor for dry period post 1970 (0.64-0.73 with spline performing worst), all overestimate (450mm to 750mm) • Flood peaks: Thiessen and Kriging systematically underestimate while IDW & spline err above and below • Semi distributed model: Thiessen did poorer

13. Implications for hydrologic modeling • Watson et al 1998: 163km2 catchment, 2D&3D splines • Mean precip 12% higher for 3D than 2D, but annual streamflow was 36% higher • Mahe et al 2008: 5 watersheds (7,-20,000km2) over a precipitation gradient, comparing 2 global datasets CRU (spline+regression) & SIEREM (kriging), GR2M model • SIEREM better Nash-Sutcliffe of daily flow by 10% over all catchments (NE 50-80%) • Both annual rainfall (821-831mm) and annual streamflowmeans similar between models, (11% differences); more different in drier catchments • Seasonal flows show more variability between models: Dry month flows varied 80%, 1cms; wet month flows (30%, 5cms)

14. Conclusions/Ideas • Different interpolation methods appear more robust in different areas or in studies with different station densities – try a variety for a local scale assessment • Watershed scale integration typically augment s the variability between methods in the flow outputs • Validation / comparison of methods tried • Scale of validation match scale of application (not so when using global pre-prepared products) • indicators used in validation and/or comparisons relevant to the use of the interpolated surface • Hydrologic applications: extremes & durations of wet/dry periods can be more important than means • There are generally fewer stations at high elevations than lower: • Use larger areas to ensure high elevation stations are included • Weight stations during validation to account for area at different elevations

15. Conclusions/Ideas • Options without local stations at a variety of elevations: • Use a more regional set of stations and multiple regression with factors like elevation and distance from the ocean for different aspect facets and apply it • Incorporate other types of data: • NDVI or other vegetation greenness • Satellite data

16. References Daly, C., R. P. Neilson, and D. L. Phillips, 1994: A statisticaltopographic model for mapping climatological precipitation over mountainous terrain. J. Appl. Meteor., 33, 140–158. Goovaerts, P. (2000), Geostatistical approaches for incorporating elevation into the spatial interpolation of rainfall, J. Hydrol., 228, 113–129 Hewitson, B.G., & R. G. Crane, 2010. Gridded Area-Averaged Daily Precipitation via Conditional Interpolation. Journal of Climate 2005; 18: 41-57 Hofstra, N. et al., 2008. Comparison of six methods for the interpolation of daily, European climate data. Journal of Geophysical Research, 113, 19 PP.   Mahe, G. et al., 2008. Comparing available rainfall gridded datasets for West Africa and the impact on rainfall-runoff modelling results, the case of Burkina-Faso. Water SA, 34(5), 529-536.   Ruelland, D. et al., 2008. Sensitivity of a lumped and semi-distributed hydrological model to several methods of rainfall interpolation on a large basin in West Africa. Journal of Hydrology, 361(1-2), 96-117.   Watson, F.G.R. et al., 1998. Large-scale distribution modelling and the utility of detailed ground data. Hydrological Processes, 12(6), 873-888.