Exploring the Effect of OccurrenceBiasAdjustment Assumptions on Hydrological Impact Modeling
Abstract
:1. Introduction
2. Data and Methods
2.1. Data
2.1.1. Observations
2.1.2. Climate Simulations
2.2. BiasAdjusting Methods
2.2.1. Quantile Delta Mapping
2.2.2. Singularity Stochastic Removal
2.2.3. Triangular Distribution Adjustment
Algorithm 1 Singularity Stochastic Removal. 

 Choose a day t (with precipitation ${x}_{t}>0.1$) randomly from the wet day time series. This day has a corresponding cumulative probability of $\xi ={F}_{{X}^{\mathrm{fs}}}\left({x}_{t}\mid x>0.1\right)$.
 Sample k from a uniform distribution on $\left[0,1\right]$. If $T\left(\xi \right)<k$, then draw ${x}_{t}$, the new value for day t, from a uniform distribution on $\left[0,0.1\right]$. ${x}_{t}$ is drawn randomly, to take into account that model simulations hardly have zero values. If $T\left(\xi \right)>k$, then repeat from step 1.
 For every dry day to be removed, choose a dry day t randomly from the dry day time series (with ${x}_{t}<0.1$) and sample k from a uniform distribution on $\left[0,1\right]$.
 Calculate $\xi =b\left(1\sqrt{1k}\right)$.
 Set ${x}_{t}={F}_{{X}^{\mathrm{fs}}}^{1}\left(\xi \right)={F}_{{X}^{\mathrm{fs}}}^{1}\left(b\left(1\sqrt{1k}\right)\mid x>0.1\right)$.
Algorithm 2 Triangular Distribution Adjustment. 

2.3. Evaluation Strategy
2.4. Calculation SetUp
3. Results
3.1. Precipitation Intensity
3.2. Precipitation Occurrence
3.3. Discharge
4. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Original Observed Values and Biases
Bias  

Index  Observed Value  Raw Climate Simulations  QDM  SSR & QDM  TDA & QDM 
${Q}_{5}$ (m^{3}/s)  2.30  0.91  −0.33  −0.33  −0.32 
${Q}_{25}$ (m^{3}/s)  3.36  1.44  0.01  0.01  0.01 
${Q}_{50}$ (m^{3}/s)  4.39  1.53  0.07  0.07  0.06 
${Q}_{75}$ (m^{3}/s)  5.72  2.50  −0.10  −0.10  −0.11 
${Q}_{90}$ (m^{3}/s)  7.83  4.73  −0.39  −0.39  −0.41 
${Q}_{95}$(m^{3}/s)  10.09  9.10  −1.05  −1.05  −1.06 
${Q}_{99}$ (m^{3}/s)  18.71  18.24  −1.93  −1.91  −1.68 
${Q}_{99.5}$ (m^{3}/s)  23.90  19.68  −0.71  0.66  0.28 
${Q}_{\mathrm{T}20}$ (m^{3}/s)  48.69  54.41  7.63  7.71  8.42 
${P}_{5}$ (mm)  0.00  0.00  0.00  0.00  0.00 
${P}_{25}$ (mm)  0.00  0.08  0.00  0.00  0.02 
${P}_{50}$ (mm)  0.10  1.01  0.05  0.05  0.04 
${P}_{75}$(mm)  2.70  1.83  −0.18  −0.18  −0.18 
${P}_{90}$(mm)  7.40  1.99  −0.26  −0.26  −0.26 
${P}_{95}$ (mm)  11.42  2.38  −0.61  −0.61  −0.61 
${P}_{99}$ (mm)  21.80  2.38  −1.86  −1.86  −1.86 
${P}_{99.5}$ (mm)  29.09  1.56  −4.20  −4.20  −4.20 
${P}_{\mathrm{P}00}$  0.65  0.00  0.00  0.00  −0.01 
${P}_{\mathrm{P}10}$  0.32  0.00  0.00  −0.00  0.02 
${N}_{\mathrm{dry}}$  3470.00  −1466.00  0.00  −17.00  43.70 
${P}_{\mathrm{lag}1}$  0.33  0.11  0.03  0.03  0.03 
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Index  Name 

P${}_{x}$  Precipitation amount percentiles, with x the percentile considered 
Q${}_{x}$  Discharge percentiles, with x the percentile considered 
Q${}_{\mathrm{T}20}$  20year return period value of discharge 
P${}_{\mathrm{P}00}$  Precipitation transition probability from a dry to a dry day 
P${}_{\mathrm{P}10}$  Precipitation transition probability from a wet to a dry day 
N${}_{\mathrm{dry}}$  Number of dry days 
P${}_{\mathrm{lag}1}$  Precipitation lag1 autocorrelation 
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Van de Velde, J.; Demuzere, M.; De Baets, B.; Verhoest, N.E.C. Exploring the Effect of OccurrenceBiasAdjustment Assumptions on Hydrological Impact Modeling. Water 2021, 13, 1573. https://doi.org/10.3390/w13111573
Van de Velde J, Demuzere M, De Baets B, Verhoest NEC. Exploring the Effect of OccurrenceBiasAdjustment Assumptions on Hydrological Impact Modeling. Water. 2021; 13(11):1573. https://doi.org/10.3390/w13111573
Chicago/Turabian StyleVan de Velde, Jorn, Matthias Demuzere, Bernard De Baets, and Niko E. C. Verhoest. 2021. "Exploring the Effect of OccurrenceBiasAdjustment Assumptions on Hydrological Impact Modeling" Water 13, no. 11: 1573. https://doi.org/10.3390/w13111573