说明

在这里插入图片描述
HBV模型包括一系列自由参数，其值可以通过率定得到。同时也包括一些描述流域和气候特征的参数，它们的值在模型率定是假定不变。子流域的划分使得在一个子流域中可能有很多参数值。虽然在大多数应用中，各子流域之间参数值只有很小的变化，但仍应慎重选取这些参数。

HBV模型主要包括三个子程序：积雪及融雪模块在上层、土壤含水量计算在中层、响应路线在底层。

可以根据流域水系拓朴结构，分别模拟各子流域的径流过程，确定各子流域产流到达总流域出口所流经的子流域，计算各子流域径流到达总流域的出口时间，最后根据汇流时间叠加总流域产流量，形成流域总出口的径流过程。

以下代码，仅包含产流部分，请酌情参考~

源代码

输入数据：逐日降水、逐日气温
输出数据：逐日产流

import numpy as np
import matplotlib.pyplot as plt

"""
Citation:
AghaKouchak A., Habib E., 2010, Application of a Conceptual Hydrologic
Model in Teaching Hydrologic Processes, International Journal of Engineering Education, 26(4), 963-973. 

AghaKouchak A., Nakhjiri N., and Habib E., 2012, An educational model for ensemble streamflow 
simulation and uncertainty analysis, Hydrology and Earth System Sciences Discussions, 9, 7297-7315, doi:10.5194/hessd-9-7297-2012.
"""


def nse_cost(p):
    """
	Purpose:
    """
    # Call HBV model
    q_sim = hbv_main(len(temp), p, temp, precip, dpem)

    # Calculate Nash-Sutcliffe Efficiency
    nse = 1.0 - (np.sum((q_obs - q_sim) ** 2.)) / (np.sum((q_obs - np.mean(q_obs)) ** 2.))
    nse = 1.0 - nse
    return nse


def hbv_main(n_days, params, air_temp, prec, dpem):
    Tsnow_thresh = 0.0
    ca = 410.

    # Initialize arrays for the simiulation
    snow = np.zeros(air_temp.size)  #
    liq_water = np.zeros(air_temp.size)  #
    pe = np.zeros(air_temp.size)  #
    soil = np.zeros(air_temp.size)  #
    ea = np.zeros(air_temp.size)  #
    dq = np.zeros(air_temp.size)  #
    s1 = np.zeros(air_temp.size)  #
    s2 = np.zeros(air_temp.size)  #
    q = np.zeros(air_temp.size)  #
    qm = np.zeros(air_temp.size)  #

    # Set parameters
    d = params[0]  #
    fc = params[1]  #
    beta = params[2]  #
    c = params[3]  #
    k0 = params[4]  #
    l = params[5]  #
    k1 = params[6]  #
    k2 = params[7]  #
    kp = params[8]  #
    pwp = params[9]  #

    for i_day in range(1, n_days):
        # print i_day
        if air_temp[i_day] < Tsnow_thresh:

            # Precip adds to the snow pack
            snow[i_day] = snow[i_day - 1] + prec[i_day]

            # Too cold, no liquid water
            liq_water[i_day] = 0.0

            # Adjust potential ET base on difference between mean daily temp
            # and long-term mean monthly temp
            pe[i_day] = (1. + c * (air_temp[i_day] - monthly[month[i_day]])) * dpem[month[i_day]]

            # Check soil moisture and calculate actual evapotranspiration
            if soil[i_day - 1] > pwp:
                ea[i_day] = pe[i_day]
            else:
                # Reduced ET_actual by fraction of permanent wilting point
                ea[i_day] = pe[i_day] * (soil[i_day - 1] / pwp)

                # See comments below
            dq[i_day] = liq_water[i_day] * (soil[i_day - 1] / fc) ** beta
            soil[i_day] = soil[i_day - 1] + liq_water[i_day] - dq[i_day] - ea[i_day]
            s1[i_day] = s1[i_day - 1] + dq[i_day] - max(0, s1[i_day - 1] - l) * k0 - (s1[i_day] * k1) - (
                    s1[i_day - 1] * kp)
            s2[i_day] = s2[i_day - 1] + s1[i_day - 1] * kp - s2[i_day] * k2
            q[i_day] = max(0, s1[i_day] - l) * k0 + (s1[i_day] * k1) + (s2[i_day] * k2)
            qm[i_day] = (q[i_day] * ca * 1000.) / (24. * 3600.)
        else:
            # Air temp over threshold: precip falls as rain

            snow[i_day] = max(snow[i_day - 1] - d * air_temp[i_day] - Tsnow_thresh, 0.)

            liq_water[i_day] = prec[i_day] + min(snow[i_day], d * air_temp[i_day] - Tsnow_thresh, 0.)

            # PET adjustment
            pe[i_day] = (1. + c * (air_temp[i_day] - monthly[month[i_day]])) * dpem[month[i_day]]

            if soil[i_day - 1] > pwp:
                ea[i_day] = pe[i_day]
            else:
                ea[i_day] = pe[i_day] * soil[i_day] / pwp

            # Effective precip (portion that contributes to runoff)
            dq[i_day] = liq_water[i_day] * ((soil[i_day - 1] / fc)) ** beta

            # Soil moisture = previous days SM + liquid water - Direct Runoff - Actual ET
            soil[i_day] = soil[i_day - 1] + liq_water[i_day] - dq[i_day] - ea[i_day]

            # Upper reservoir water levels
            s1[i_day] = s1[i_day - 1] + dq[i_day] - max(0, s1[i_day - 1] - l) * k0 - (s1[i_day] * k1) - (
                    s1[i_day - 1] * kp)
            # Lower reservoir water levels
            s2[i_day] = s2[i_day - 1] + dq[i_day - 1] * kp - s2[i_day - 1] * k2

            # Run-off is total from upper (fast/slow) and lower reservoirs
            q[i_day] = max(0, s1[i_day] - l) * k0 + s1[i_day] * k1 + (s2[i_day] * k2)
        # Resulting Q
        qm[i_day] = (q[i_day] * ca * 1000.) / (24. * 3600.)

    # End of simulation
    return qm


def main(calibrate=False):
    # =======================================================================

    # Calibration Flag - *Set to 'True' during calibration to prevent plotting

    # Read paramter values
    para_init = np.genfromtxt('params_calibrate.dat', skip_header=1, usecols=[1], unpack=True)

    if calibrate:
        pass
    else:
        q_sim = hbv_main(len(temp), para_init, temp, precip, dpem)
        plt.plot(q_obs, label='Q_obs', color='blue')
        plt.plot(q_sim, label='Q_sim', color='red', ls='--')
        plt.legend(fontsize=10)
        plt.ylabel('Stream Flow [cms]', fontsize=10)
        plt.xlabel('Number of Days from Run Start', fontsize=10)
        plt.tight_layout()
        plt.show()

    model_error = nse_cost(para_init)

    f_out = open('model_err.dat', 'w+')
    f_out.write(str(model_error) + '\n')
    f_out.close()


if __name__ == '__main__':
    # Read Input (Air Temp.,PET, Precip.)
    month, temp, precip = np.genfromtxt('inputPrecipTemp.txt', usecols=[1, 2, 3], unpack=True)
    monthly, tpem, dpem = np.genfromtxt('inputMonthlyTempEvap.txt', unpack=True)
    month = month.astype(int)
    # Read Q observed
    q_obs = np.genfromtxt('Qobs.txt')
    main()