A literature review of interpolated precipitation surfaces &

implications for watershed modeling

Julia Glenday7 May 2010

Presentation outline

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

Background/MotivationGoal: 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?

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

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Govaaerts, 1999

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 Precipitation Climatology Center (WMO) - kriging

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)

PRISM: Precipitation-elevation Regressions on Independent Slopes Model

(Daly et al 1994, 2000)Process:• Use a DEM to group stations into topographic facets

– Factets based on slope orientation – coarsen until reach threshold number of stations per facet

• Create and apply a localized regression of precipitation vs elevation & or coastal proximity for a local radius within a facet– stations assigned to DEM elevations for regression: assume that fine scale

topography has less effect than broad scale features

Addresses:• Effects of elevation on precip• Spatial scale & pattern of orographic effects

Needs high station density to improve on other methods, doesn’t account for other local factors of influence, or temporal variability in elevation relationship

Conditional interpolation (Hewitson & Crane, 2005)

Process:• Within a radius of target cell use pattern of station

values to derive synoptic atmospheric ‘states’ – using Self Organizing Maps as a clustering method

• Use the pattern of wet/dry stations during each synoptic ‘state’ to make a wet/dry probability surface (done similarly to Kriging)

• Within areas predicted to be wet for the day’s state, interpolate from stations

• Create this surface at fine grid (0.1o), then coarsen itAddresses:• Non continuity of precipitation – very important at the daily scale• Distance-decay functions: state specific & states and the temporal pattern

of states are determined by patterns in the data (rather than making monthly relationships, etc)

Needs high station density to improve on other methods, elevation implicitly dealt only given high station density

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 topo var, 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 kriging and 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. Kriging performed best on average over the region (Hofstra 2008)

Implications for hydrologic modelingDepends 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

Implications for 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 ave ppt: 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

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

streamflow means 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)

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

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

ReferencesDaly, 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, 113–129Hewitson, B.G., & R. G. Crane, 2010. Gridded Area-Averaged Daily Precipitation via Conditional Interpolation.

Journal of Climate 2005; 18: 41-57Hofstra, 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.