Comparing the Effects of Different Daily and Sub-Daily Downscaling Approaches on the Response of Urban Stormwater Collection Systems

Abstract

Change in the spatiotemporal pattern of precipitation is one the most important effects of climate change. This may result in considerable changes in urban flooding and yield a variation in the rate and volume of stormwater, resulting in the failure of stormwater collection systems. In the current paper, the effects of different downscaling methods on a built urban network have been assessed and compared. The case study is a 320-ha urban watershed with a built stormwater collection system located in the City of Tehran, Iran. Two single (SDSM and DMDM) and two multisite downscaling techniques with a daily temporal resolution have been employed and two sub daily (based of GEV distribution and MOF) methods have been used to further disaggregate the downscaled data. To evaluate the climate change impacts, three climate change scenarios, i.e. RCP 2.6, RCP 4.5 and RCP 8.5, have been used. Based on our findings, DMDM appears to outperform the other techniques in terms of our statistical similarity and dissimilarity metrics for daily downscaling. In addition, the sub-daily disaggregation method via GEV distribution delivers better results in comparison to the MOF. After simulating the stormwater collection system based on the downscaling results, we found that the number of flooded channels and junctions using RCP 8.5 results is significantly higher than RCP 4.5 and RCP 2.6 scenarios, indicating the relatively high risk of urban flooding under RCP 8.5 scenario.

Appendices

Appendix 1

Table 8 The NCEP predictors

Table 9 Coefficients R², MAE, and RMSE between the monthly means of the observed and simulated daily precipitation by different downscaling methods during the calibration period

Table 10 Coefficients R², MAE, and RMSE between the monthly means of the observed and simulated daily precipitation by different downscaling methods during the validation period

Table 11 Results of combined different daily and sub-daily downscaling methods in calibration period

Appendix 2

1.1 Sub Daily Downscaling

1.1.1 Sub Daily Downscaling based on GEV Distribution

The first approach to sub daily downscaling is based on a triple-parameter GEV distribution which is familiar with two fold-parameter Gumbel distribution. Nguyen et al. (2007) estimated precipitation intensity to inferred IDF curves using GEV distribution based on the scale-invariance concept. They introduced this statistical approach as a proper tool in statistical analysis of extreme events.

GEV distribution has three scale(α), shape(k), and location (ϵ) parameters to be estimated by Non-Central Moment (NCM) method (Eq. B-1 to B-3).

$$ E(H)=\left(\epsilon +\frac{\alpha }{k}\right)\hbox{--} \left(\frac{\alpha }{k}\right)\varGamma \left(k+1\right) $$

(B-1)

$$ E\ \left({H}^2\right)={\left(\epsilon +\frac{\alpha }{k}\right)}^2\kern0.5em \hbox{--} 2\ \left(\frac{\alpha }{k}\right)\left(\epsilon +\frac{\alpha }{k}\right)\varGamma \left(k+1\right)+{\left(\frac{\alpha }{k}\right)}^2\varGamma \left(2k+1\right) $$

(B-2)

$$ E\ \left({H}^3\right)={\left(\epsilon +\frac{\alpha }{k}\right)}^3-3\ \left(\frac{\alpha }{k}\right){\left(\epsilon +\frac{\alpha }{k}\right)}^3\varGamma \left(k+1\right)+3{\left(\frac{\alpha }{k}\right)}^2\left(\epsilon +\frac{\alpha }{k}\right)\varGamma \left(2k+1\right)-{\left(\frac{\alpha }{k}\right)}^3\varGamma \left(3k+1\right) $$

(B-3)

where H, is yearly time series of maximum daily precipitation or different sub-daily durations, E is the mathematical expectation of the time series, and Γ is gamma function. According to the scaling invariance concept, k is constant for different precipitation durations (Eq. B-7). By using λ^β (Eq. B-4) which is calculated in different sub-daily durations (in calibration period), location(ϵ) and scale(α) parameters related to sub-daily duration in future scenarios are estimated (Eq. B-5 and B-6), where ${\mu}_{1_t}$ and ${\mu}_{\lambda_t}$ are average of maximum yearly precipitation time series in calibration period during one day and λ percent of a day (0<λ<1), respectively. Further details of the approach are presented in Fig. 10 and can be found at Nguyen et al. (2007).

$$ {\lambda}^{\beta }=\frac{\mu_{1_{\lambda t}}}{\mu_{1_t}} $$

(B-4)

$$ \alpha \left(\lambda t\right)={\lambda}^{\beta}\alpha (t) $$

(B-5)

$$ \epsilon \left(\lambda t\right)={\lambda}^{\beta}\epsilon (t) $$

(B-6)

$$ \epsilon \left(\lambda t\right)={\lambda}^{\beta}\epsilon (t) $$

(B-7)

Fig. 10

Schematic diagram of GEV based on scaling invariance concept.

1.1.2 Sub Daily Downscaling based on MOF

The concept of non-parametric method of fragment is based on disaggregating the day of interest using candidate day’s fragments in historical time series (Mezghani and Hingray 2009). In this paper single site sub-daily downscaling method proposed by Li et al., (2018) was deployed. Main steps of MOF are as follow (Fig. 11):

• calculation sub-daily fragment vector for interested day i,

$$ {F}_i=\left\lceil {f}_{i,1},{f}_{i,2},\dots, {f}_{i,j},\dots, {f}_{i,m}\right\rceil $$

(B-8)

$$ {f}_{i,j=}\frac{X_{i,j}}{\sum_{j=1}^m{X}_{i,j}} $$

(B-9)

In Eq. B-B-8 and B-B-9, f_{i, j} is fragment related to the i^th day and j^th duration, X_{i, j} is sub-daily precipitation event (in calibration period).

• Daily precipitation (P_i) and its Fragment vector (F_i) are classified into classes based on the magnitude of P_i.

• To disaggregate P_t (simulated daily precipitation at day t), the corresponding class to it (C_t) specified.

• Through fragment vectors related to class C_t, data with same last-day and next-day wetness state with P_t are selected.

• One of the fragment vectors, generated in previous step is selected randomly (step *)

• Sub daily precipitation vector, H is calculated (Eq. B-10) as the product of daily precipitation P′_t multiplied by selected fragment vector (step **)

$$ H=P{\prime}_t\ast F{\prime}_i $$

(B-10)

• Steps * and ** will be continued up to the number of defined ensembles.

Fig. 11

Schematic diagram of MOF

1.2 Statistical Evaluation

In order to evaluate and compare different sub-daily and daily downscaling methods, different statistical indicators have been used in this study. Coefficient of determination (R²), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) based on monthly mean are used, which are given by following equations (Eq. B-11 to B-13).

$$ {R}^2=1-\frac{\sum_{i=1}^t{\left({X}_{obs,i,k}-{X}_{Sim,i,k}\right)}^2}{\sum_{i=1}^t{\left({X}_{Obs,i,k}-{\overline{X}}_{Obs}\right)}^2} $$

(B-11)

$$ MAE=\frac{1}{t}\sum \limits_{i=1}^t\left|{X}_{obs,i,k}-{X}_{Sim,i,k}\right| $$

(B-12)

$$ RMSE=\sqrt{\frac{1}{t}\sum \limits_{i=1}^t{\left({X}_{obs,i,k}-{X}_{Sim,i,k}\right)}^2} $$

(B-13)

where t is the length of daily time series, X_{obs, i, k} and X_{sim, i, k} are the observed value and simulated value in the calibration period at day i and station k respectively and ${\overline{X}}_{obs}$ is mean of observed values. The closer MAE and RMSE are to zero, the more accurate the model is in simulating the given variable. Also in R², values closer to 1 are representative of better performance of the model in simulating the given variables.