结果评价

According to Boyle et al. (2000),（Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods. Water Resources Res. 36(12): 3663-3674.）

optimizing RMSE during model calibration may give small error variance but at the expense of significant model bias。因此需要综合考虑。

The Nash–Sutcliffe Efficiency (NSE), which measures the model fit primarily during high-flow periods;

The Box-Cox transformed root mean squared error (TRMSE), which accounts for low-flow periods;

The Mean Squared Derivative Error (MSDE) indicator of the fit of the hydrograph shape;

The runoff coefficient error (ROCE), which accounts for the long-term water balance.

Python代码：

# Calculate NSE - Nash-Sutcliffe Efficiency coefficient
def NSE3(obs,mol,k):
    numerator = 0
    denominator = 0
    meangauge = 0
    for i in range(len(obs)):
        numerator+=pow(abs(mol[i][k])-obs[i],2)
        meangauge+=obs[i]
    meangauge=meangauge/len(obs)
    for i in range(len(obs)):
        denominator+=pow(obs[i]-meangauge,2)
    return 1-numerator/denominator

def NSE(obs,mol):
    numerator = 0
    denominator = 0
    meangauge = 0
    for i in range(len(obs)):
        numerator+=pow(abs(mol[i])-obs[i],2)
        meangauge+=obs[i]
    meangauge=meangauge/len(obs)
    for i in range(len(obs)):
        denominator+=pow(obs[i]-meangauge,2)
    return 1-numerator/denominator

# Calculate TRMSE - The Box-Cox transformed root mean squared error
def TRMSE3(obs,mol,k):
    trmse = 0
    for i in range(len(obs)):
        zmdl = (pow((abs(mol[i][k])+1),0.3)-1)/0.3
        zobs = (pow((abs(obs[i])+1),0.3)-1)/0.3
        trmse+=pow(zmdl-zobs,2)
    return pow(trmse/len(obs),0.5)

def TRMSE(obs,mol):
    trmse = 0
    for i in range(len(obs)):
        zmdl = (pow((abs(mol[i])+1),0.3)-1)/0.3
        zobs = (pow((abs(obs[i])+1),0.3)-1)/0.3
        trmse+=pow(zmdl-zobs,2)
    return pow(trmse/len(obs),0.5)

# Calculate MSDE - Mean square derivative error
def MSDE(obs,mol,k):
    msde = 0
    for i in range(1,len(obs)):
        msde+=pow(((obs[i]-obs[i-1])-(mol[i][k]-mol[i-1][k])),2)
    return msde/len(obs)

# Calculate ROCE - the runoff coefficient error
def ROCE(obs,mol,k):
    summdl = 0
    sumobs = 0
    for i in range(len(obs)):
        summdl+=mol[i][k]
        sumobs+=obs[i]
    return abs(summdl-sumobs)/sumobs

NSE——Nash-Sutcliffe efficiency coefficient

（或简称Ens：注意ns是下标！）

http://blog.sciencenet.cn/home.php?mod=space&uid=350729&do=blog&id=1080236&from=space

公式中：Qo指观测值，Qm指模拟值，Qt（上标）表示第t时刻的某个值，Qo(上横线)表示观测值的总平均。

1-噪音/信息（实测值）

E取值为负无穷至1，E接近1，表示模式质量好，模型可信度高；
E接近0，表示模拟结果接近观测值的平均值水平，即总体结果可信，但过程模拟误差大；
E远远小于0，则模型是不可信的。

TRMSE——Box-Cox Transformed Root Mean Squared Error

经B-C转换后的RMSE均方根误差：

Box-Cox变换的目的是为了让数据满足线性模型的基本假定，即线性、正态性及方差齐性。
均方根误差亦称标准误差,它是观测值与真值偏差的平方与观测次数比值的平方根。均方根误差是用来衡量观测值同真值之间的偏差。标准误差对一组测量中的特大或特小误差反映非常敏感，所以，标准误差能够很好地反映出测量的精密度。可用标准误差作为评定这一测量过程精度的标准。

均方根误差（或称方均根偏移、均方根差、方均根差等，英文：root-mean-square deviation、root-mean-square error、RMSD、RMSE）

均方根误差代表模拟值和观察值之差的样本标准差（sample standard deviation），当这些差值是以资料样本来估计时，他们通常被称为残差；当这些差值不以样本来计算时，通常被称为预测误差（prediction errors）。
RMSE is always non-negative, and a value of 0 (almost never achieved in practice) would indicate a perfect fit to the data. In general, a lower RMSD is better than a higher one.
对异常值很敏感，因此能够表示模拟精度；
预测值与真实值偏差的平方与观测次数n比值的平方根。