Azadeh Ramesh 1 , Alireza Shahabfar 2

1. Construction of a Flood Risk Management System in a Watershed by Using Statistical Models (Case Study: Kardeh Watershed) Azadeh Ramesh1, Alireza Shahabfar2 1. Msc. of Geography, North Khorasan Meteorological Administration, I.R.of Iran Meteorological Organization (IRIMO) 2. Msc. of Civil Engineering, North Khorasan Meteorological Administration, I.R.of Iran Meteorological Organization (IRIMO)

2. drought and flood Introduction By occurrence of climate change phenomenon and increasing of human’ s interference on global climate, two natural disasters such as: have effected on different parts of the earth. In the recent years, our country was alternatively witness in occurring of floods and severe droughts in most of places, specially occurring of these natural disasters together, improve each other as because of severe droughts, vegetative coverage and humidity of soil are spoiled that is facilitation agent for flowing destructive floods. On the other hand, occurring of severe floods have caused destroyed of agricultural lands and leaching of fertile soils and have amplified the effective of drought in these places.

3. In a watershed which has high submergible potential, with an alternative and correct management, we can reduce the effects and damages of flood and use of it for increasing of water potential , for example by: • increasing of soil moisture • discharging of aquifer • increasing of water resources of lake of dams. For succession in these actions, an alternative and optimum flood risk management in that watershed is necessary.

4. This research has focused on understanding the nature of likely changes in flood risk across the Iran ‎and in the North Khorasan: The location of Kardeh basin over the map

5. Statistical Models of Climate Variability To study the impact of different representations of climate variability on flood risk assessment and project evaluation, this paper considers 3 reasonable models that can forecast flood risk: 1- Log-Normal i.i.d. Model (LN i.i.d.) 2- Log-Normal Trend Model (LN Trend) 3- Log-Normal ARMA Model (LN ARMA)

6. m d2 log( Q ) ~ N ( , ) t 1- Log-Normal i.i.d. Model (LN i.i.d.) This model assumes that the maximum annual floods (Qt) are independent and identically distributed random variables where: In this equation; Qt: Maximum annual flow for year t. : Log scale mean of the maximum annual flow : Long run standard deviation This is a traditional model used for flood risk management.

7. = m + l - + e log( Q ) * ( t t ) t t 2- Log-Normal Trend Model (LN Trend) This model assumes that the maximum annual floods (Qt)have a log normal distribution around a linear trend, so that, In this equation; Qt : Maximum annual flow for year t. : Log scale mean of the maximum annual flow : Log scale slope of the trend in the Log-Normal trend model T : Year index t : Year index t: Average of years in the design period : Error process

8. - m log( Q ) ~ ARMA ( p , q ) t 3- Log-Normal ARMA Model (LN ARMA) This model assumes that the maximum annual floods (Qt) are generated by a stationary low-order Autoregressive Moving-Average process ARMA (p,q) for the log-flood series: In this equation; Qt : Maximum annual flow for year t. : Log scale mean of the maximum annual flow ARMA : Auto Regressive Moving-Average p: order of Auto Regressive q: order of Moving-Average

9. Risk Forecasts for The Kardeh Basin

10. For the LN i.i.d. model , threshold is a straight horizontal line that was almost exceeded in 2005. The LN i.i.d. model predicts the lowest risk levels over the design period. 1- Log-Normal i.i.d. Model (LN i.i.d.) Mean and 20-years flood levels over historical and planning period for Kardeh record ‎using three flood risk models

11. For the LN Trend model the 2% exceedance threshold is a straight line with a positive slope and it extends from 1984 to 2001 for LN Trend (Ts) and from 1984 to 2005 for LN Trend (Tc). The Log-Normal model with the assumption that the trend continues, LN Trend/Tc, includes the statistically significant positive trend (= 0.3119) . as a result the forecasted exceedance probability would converge eventually to 1. Because  is small, this happens slowly and for the design period (20 years) the results may be unreasonable. This model predicts the highest risk over the planning horizon. LN Trend/Ts predicts lower flooding risks than the LN Trend/Tc model, but higher risk levels than the LN i.i.d. and LN ARIMA models. 2- Log-Normal Trend Model (LN Trend) Mean and 20-years flood levels over historical and planning period for Kardeh record ‎using three flood risk models

12. the ARIMA(1,2,3) model conditional mean forecast delays to the long-term mean after a decade or so. For the mean, the linear variation extends from 1984 to 2005 .The LN ARIMA(1,2,3) model forecasts flood risk as an average of the long-run unconditional risk and the risk in the last years of record. Because the last years of record at Kardeh experienced several large floods, the predicted annual flood tends to be much higher than the long-run unconditional mean. The LN ARIMA(1,2,3) model is very responsive to the observed values at the end of the record. It would predict lower risks than the LN i.i.d. model if the last years of record experienced only smaller floods. 3- Log-Normal ARMA Model (LN ARMA) Mean and 20-years flood levels over historical and planning period for Kardeh record ‎using three flood risk models

13. Management of flood risk in a world with variable climate would be aided by simple summary measures of flood risk. A set of such simple risk measures was developed and used to compare three risk forecasts. The investigation demonstrated that stationary time series models are very flexible and produce a reasonable interpretation of historical records. The i.i.d. model is included within this larger class of models. Stationary time series allow risk to vary but preserve the assumption that hydrology is stationary in the long run. In this framework, perceived trends in a flood record can be interpreted as the result of natural and stationary variations. When stationary time series models are used for risk forecasting, the predicted risk returns to the unconditional long run average as the forecasting horizon is extended. The resulting variation in flood risk is likely to affect flood risk management if decision parameters can be adjusted on a year-to-year basis; however variations in flood risk are likely to have disappeared before major construction projects can be designed, authorized and completed.

14. Conclusions

15. In this research we consider three simple statistical models :1- LN i.i.d Model 2- LN Trend Ts & Tc Model 3- LN ARIMA.As a result we understand that: • 1) LN i.i.d model have large conclusion and have no economic benefits and amount of flood risk is permanent per time so the result of this model isn't logical. • 2) LN Trend Ts and LN Trend Tc models have not actual conclusion because it doesn't consider climate variability and application of this conclusion isn't possible in actual conditions and they don't offer acceptable responses because they obey from one general trend. • 3) LN ARIMA model doesn’t have disadvantages of previous models and it's results are very reasonable and argumentative for predictions and simulations of flood risk in Kardeh basin. But, we must consider that we can use time series model just for one or two time steps and applications of long predictions in this model isn't valuable and in this conditions we must update the model by replacing of observed data instead of simulated values. Therefore, by considerations of advantage and disadvantage, this model is very suitable and useful for Kardeh basin.

16. Thank you for attention