Institut für Wasser- und Umweltsystemmodellierung Lehrstuhl für Hydrologie und Geohydrologie Prof. Dr. rer. nat. Dr.-Ing. András Bárdossy Pfaffenwaldring 61, Stuttgart, Deutschland Universität Stuttgart Simultaneous calibration of hydrological models to capture non-stationary conditions András Bárdossy & Yingchun Huang

2 Introduction Non stationary conditions: –Input: Weather – Climate –Properties: Land use How to cope: –Temporal (limited in extent) –Spatial (limited in similarity) Similarity vs. Self similarity

Modelling Model calibration – parameter estimation –Known input and output Select a model Select performance criteria (NS, GK, Multiobjective) Optimization principle –Search a single optimum –Search a set of optima (equifinality) Model „Validation“ –Known input and output Test calibration parameters on a different case

Goals To capture the essential features –Transferable to different conditions –Modelling is not repeating what was observed

The tools Models –HBV –Hymod –Xianjiang Performance –NS –KG –NS+LogNS Calibration method –ROPE – depth based calibration (Half space depth) with a set of optima (represented by pars.)

ROPE MC step Selection step (Best 15%)

Monte Carlo of the deep in the selected

Select best 15%...

Location of the study area 15 selected catchments ( km 2 )

Weather is not stationary ( ) 10 year mean values –0.5C difference between the mean values –Up to 40 % difference in precipitation Investigate transfer from one time period to the other –10 years intervals starting 1950

Model performance –Strongly dependent of the application period –Weakly dependent on the calibration period Bad news – we can only modify calibration For 8 catchments all calibrations transfer well for all periods good guys For 3 catchments many transfers are problematic bad guys

Optimal performance –For the given „distribution“ of weather Same weather different frequencies  different parameters –Parameter estimation „for any weather distribution“ Distribution from other time periods (Time) Distribution from other catchments (Space)

Method 1 -Time Adjust weather of the calibration period –Emphasize years with weather similar to target Known for observed periods „Given“ for climate change –Reshuffling not possible due to discharge observations –Weighting

Weighted objective function

Simple trick Little but positive effect –Better transfer of the model parameters Mean – most cases Minimum nearly always –Catchment applied for 1970s NS  0.526

Method 2 - Space There are other catchments which experienced different (target) weather (German weather will be like Italian) –Take a similar catchment and use it –What is similar? –How to use it?

Similar – if common parameters work well in the calibration period Common parameters obtained via common calibration Parameters which are good for all catchments

Pairwise application C=2 –All good for all bad –Similarity over the calibration periods –If common calibration does not deteriorate calibration quality then similar

Transfer Calibration application

Gain in the average for catchment 4

Gain in the average for catchment 9

Gain in the minimum for catchment 4

Gain in the minimum for catchment 11

Method 2 results Common calibration improves transfer quality if similar catchments are used Similarity can be recognized Minimum performance is strongly improved –low risk of failure

Other possibilities Common calibration with C>2 Filtering observation errors –Bias –Random errors Common calibration for land use change –Using implicit assumptions –Assigning parameter(s) to land use and calibrate individually

Summary A good model should work under all conditions  transferability Transferability is mainly receiver dependent Transferability can be improved –Using a weather mix (weights) –Using other catchments via common calibration

Does this matter at all?

10 years + 1 C o scenario

Thank you!