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--- projects:streamflow_uncertainty_analysis_using_crawford_model_and_mc [2025-01-04 02:15 pm] – [Plotting the results] um
+++ projects:streamflow_uncertainty_analysis_using_crawford_model_and_mc [2025-01-08 02:34 pm] (current) – removed hcho
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-==== Streamflow Uncertainty Analysis Using Crawford Model and MC ====
-**1. Model Overview**
-{{:workspaces:crawford_model.jpg?400 |}}
-The Crawford model is a hydrological model used to estimate streamflow by simulating the water balance in a watershed. It incorporates rainfall, evapotranspiration, soil moisture, and groundwater flow to predict runoff and discharge. The model is particularly useful for analyzing the impact of climate and land use changes on water resources. The conceptual model is presented in the adjacent figure.
-**2. Input Parameters**
-The input parameters and initial parameters are presented below. The Monthly precipitation data is prepared using thession polygon. The potential evapotranspiration is calculated using the Penman-Monteith equation. The monthly observed discharge is the stream flow value of the considered gauge station.
-==== Code for Input Parameters ====
-<input file Python>
-    import numpy as np
-    # Given Data
-    p_sub = 0.6
-    Gwf = 0.45
-    annual_ppt = 2026
-    C = 0.25
-    nominal = 400
-    ground_storage = 17.5  # This is the initial groundwater storage
-    initial_soil_moisture_storage = 350  # January initial value
-    initial_ground_water_storage = 17.5  # Initial groundwater storage in January
-    # Monthly PPT and PET data
-    monthly_ppt = [0.299, 3.585, 18.744, 86.719, 312.905, 461.040, 673.795, 668.385, 325.471, 10.699, 0.665, 0.000]
-    monthly_pet = [16.120, 25.507, 45.706, 72.145, 86.949, 85.707, 74.120, 65.469, 74.508, 51.072, 25.309, 13.315]
-    #Monthly observed discharge at Gaurighat gauge station
-    monthly_obs_discharge = [0.27, 0.22, 0.18, 0.26, 1.24, 2.64, 7.47, 11.7, 6.17, 2.19, 1.87, 0.70]
-==== Crawford Model ====
-This is the main part of the model. This simulates the discharge considering the parameters passed to it.
-<Model Preparation>
-    import numpy as np
-    import matplotlib.pyplot as plt
-    # Function encapsulating your discharge calculation logic
-    def calculate_discharge(p_sub, Gwf, annual_ppt, C, nominal, ground_storage,
-                        initial_soil_moisture_storage, initial_ground_water_storage,
-                        monthly_ppt, monthly_pet, area):
-    soil_moisture_storage = [initial_soil_moisture_storage]
-    final_ground_storage = [initial_ground_water_storage]
-    direct_flow = []
-    groundwater_flow = []
-    total_discharge = []
-    ppt = monthly_ppt[i]
-    pet = monthly_pet[i]
-    for i in range(12):
-    # 1. Storage Ratio
-        storage_ratio_val = soil_moisture_storage[-1] / nominal
-        # 2. PPT/PET Ratio
-        ratio_ppt_pet_val = ppt / pet if pet != 0 else 0
-        # 3. AET/PET Ratio
-        if ratio_ppt_pet_val > 1:
-            ratio_aet_pet_val = 1
-        elif ratio_ppt_pet_val >= 2:
-            ratio_aet_pet_val = 0
-        else:
-            ratio_aet_pet_val = (1 - storage_ratio_val / 2) * ratio_ppt_pet_val + storage_ratio_val / 2
-        # 4. AET
-        aet_val = ratio_aet_pet_val * pet
-        # 5. Water Balance
-        water_balance_val = ppt - aet_val
-        # 6. Excess Moisture Ratio
-        excess_moisture_ratio_val = 1 / (1 + np.exp(-5.03 * (storage_ratio_val - 1)))
-        # 7. Excess Moisture
-        excess_moisture_val = water_balance_val * excess_moisture_ratio_val if water_balance_val > 0 else 0
-        # 8. Recharge to GW
-        recharge_to_gw_val = excess_moisture_val * p_sub
-        # 9. Delta Storage
-        delta_storage_val = -excess_moisture_val + water_balance_val
-        # 10. Soil Moisture Storage
-        soil_moisture_storage_val = soil_moisture_storage[-1] + delta_storage_val
-        # 11. Initial Groundwater Storage
-        if i == 0:
-            initial_gw_storage = ground_storage
-        else:
-            initial_gw_storage = final_ground_storage[-1] - groundwater_flow[-1]
-        # 12. Final Groundwater Storage
-        final_gw_storage_val = recharge_to_gw_val + initial_gw_storage
-        # 13. Direct Flow
-        direct_flow_val = excess_moisture_val - recharge_to_gw_val
-        # 14. Groundwater Flow
-        ground_water_flow_val = final_gw_storage_val * Gwf
-        # 15. Total Discharge
-        total_discharge_val = direct_flow_val + ground_water_flow_val
-        # Append the values to their respective lists
-        soil_moisture_storage.append(soil_moisture_storage_val)
-        final_ground_storage.append(final_gw_storage_val)
-        direct_flow.append(direct_flow_val)
-        groundwater_flow.append(ground_water_flow_val)
-        total_discharge.append(total_discharge_val)
-    # Convert to cubic meters per second
-    cal_discharge = [x * (area * 1000 / 31 / 24 / 60 / 60) for x in total_discharge]
-    return cal_discharge
-==== Monte Carlo Simulation ====
-In this portion random values are generated based on the user assumptions. The radnodm values are generated for the seven different parameters.
-  * 1. Monthly ppt
-  * 2. Monthly pet
-  * 3. P_sub
-  * 4. Gwf
-  * 5. Initial_Soil_moisture_storage
-  * 6. Initial_ground_water_storage
-  * 7. nominal
-<Code for MC Smulation>
-    # Monte Carlo Simulation
-    no_of_simulations = 1000  # Number of Monte Carlo iterations
-    results = []
-    for _ in range(no_of_simulations):
-        # Para-1: Randomly generating monthly ppt data with 20% variation
-        sampled_monthly_ppt = np.random.normal(monthly_ppt, 0.2 * np.array(monthly_ppt))
-        # Assuming 20% variation
-        # Para-2: Randomly generating monthly pet with 20% variation
-        sampled_monthly_pet = np.random.normal(monthly_pet, 0.2 * np.array(monthly_pet))
-        # Assuming 20% variation
-        # Para-3, Para-4: Randomly generate uniform distributions for p_sub and GWF
-        sampled_p_sub = np.random.uniform(0.5, 0.7)  # Uniform between 0.5 and 0.7
-        sampled_GWf = np.random.uniform(0.4, 0.5)    # Uniform between 0.4 and 0.5
-        # Para-5, Para-6, Para-7: Randomly generate other parameters with uniform distributions
-        sampled_initial_soil_moisture_storage = np.random.uniform(300, 400)  # Uniform between 300 and 400
-        sampled_initial_ground_water_storage = np.random.uniform(15, 25)    # Uniform between 15 and 25
-        sampled_nominal = np.random.uniform(350, 450)  # Uniform between 350 and 450
-        discharge = calculate_discharge(
-        sampled_p_sub, sampled_GWf, annual_ppt, C, sampled_nominal, ground_storage,
-        sampled_initial_soil_moisture_storage, sampled_initial_ground_water_storage,
-        sampled_monthly_ppt, sampled_monthly_pet, 74.20
-    )
-    results.append(discharge)
-    # Analyze the results (e.g., calculate means and confidence intervals)
-    results = np.array(results)
-    mean_discharge = np.mean(results, axis=0)
-    std_discharge = np.std(results, axis=0)
-==== Plotting the results====
-<Code for result visualization>
-    # Plot the results
-    months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep', 'Oct', 'Nov', 'Dec']
-    plt.figure(figsize=(10, 6))
-    plt.plot(months, mean_discharge, label='Mean Discharge', marker='o', color='green')
-    plt.fill_between(months, mean_discharge - std_discharge, mean_discharge + std_discharge,
-                 color='green', alpha=0.2, label='±1 Std Dev')
-    #plt.plot(months, monthly_obs_discharge, label='Observed Discharge', marker='o', color='blue')
-   # Adding labels and title
-   plt.xlabel('Month')
-   plt.ylabel('Discharge (m³/s)')
-   plt.title('Monte Carlo Simulation: Discharge Uncertainty')
-   plt.legend()
-   {{:workspaces:mc_plot.png?400 }}