1. Inconsistency in Chinese solar radiation data caused by instrument replacement: Quantification based on pan evaporation observations
Hanbo YANG*, Zhe Li, Mingliang Li, and Dawen Yang State key Laboratory of Hydro-Science and Engineering & Department of Hydraulic Engineering, Tsinghua University, Beijing, China *
Let
1. Introduction
4. Inconsistency in solar radiation observation
T is the transpose operator
Eio is the observed pan evaporation at the ith day
Solar radiation determines our climate and hydrological cycle, and it has been widely measured by pyrometers at meteorological stations. In the early 1990s, a large-scale instrument replacement occurred across China, leading to inconsistent solar radiation observations. Fortunately, China has consistent pan evaporation (Epan) observations from Chinese micro-pans (with a diameter of 20 cm) from the 1950s to 2001.
Therefore, we parameterized the PenPan-20 model for estimating Epan from the D20 pans using climatic factors as input, along with a Bayesian approach, and further evaluated the inconsistency in solar radiation observations based on Epan data.
There is a good agreement between Epan_cal and Epan_cal and during , but a large bias during
We assume that the error in Epan_cal caused by the overestimation of Rs can be estimated as 0.26 – 0.04 = 0.22 mm/d. The standard deviation (±0.08 mm/d) from 1961 to 1992 can approach the uncertainty in PenPan-20. As a result, from 1993 to 2001, the overestimation of Epan_cal can be estimated as 0.22±0.08 mm/d.
Eic is the calculated pan evaporation
using PenPan-20 at the ith
The model residuals,
obey a standard normal distribution N (0, τ)
The Bayesian model can be written as
The likelihood function:
R is the correlation coefficient matrix
of the model residual
The prior distributions:
a ~ U(0.1, 3.0), b ~ U(0.0, 20.0), c ~ U(1.0, 20.0), and d ~ U (0.0, 3.0)
τ ~ Γ(0.001, 0.001)
Fig.4 Trends in the observed and calculated pan evaporation during (A) 1961–2001, (B) 1961–1992, and (C) 1993–2001. Epan_obs represents the observed pan evaporation, Epan_cal represents the calculated pan evaporation using the PenPan-20 model.
2. Data and Method
Daily meteorological data were collected from 54 stations during Because of the large-scale replacement of solar radiation instruments, solar radiation has been measured with the new instruments since 1993.
The conditional PDFs:
Fig.5 Comparison between the calculated and observed pan evaporation and (B) relationship between solar radiation and sunshine hours during 1961–1992 and 1993–2001
3. PenPan-20 model and evaluation
The Markov chains of the four parameters converging after ~1,300 iterations, when a approaches 1.1, b approaches 2.7, c ~ 14.1, and d ~ 0.31 (see Fig.2), i.e.
We assumed that the difference between the observed Epan_obs and the calculated Epan_cal is caused by the inconsistency in the solar radiation observations
Fig.1 54 meteorological stations in this study
PenPan-20 model was firstly parameterized by Yang and Yang (2012) for estimating evaporation from Chinese micro-pans. However, due to the lack of sufficient experimental observations for the D20 pans, Yang and Yang (2012) assumed that the radiation reaching the water surface and pan surface had the same impact on the pan evaporation. Therefore, we parameterized the PenPan-20 by using a Bayesian approach.
is the partial differential of the PenPan-20 model, and it was estimated as
There is agreement between the observed and calculated values at the 54 stations (R2 = 0.94, n = 17,846, and RMSE = 24 mm/month) (see Fig.3).
Therefore, the overestimation of Rs during can be inferred as
(0.22±0.08)/0.16 = 1.4±0.5 MJ/(d m2),
or ~16±7 W/ m2
Best fit regression: y = 0.92 x
Reference
Li, M. L., D. W. Yang, J. S. Chen, and S. S. Hubbard (2012), Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework, Water Recourses Research, 48, W08510, doi: /2010WR
Yang, H. B., and D. W. Yang (2012), Climatic factors influencing changing pan evaporation across China from 1961 to 2001, Journal of Hydrology, 414,
Yang H. B., Z. Li, M. L. Li, and D. W. Yang (2015). Inconsistency in Chinese solar radiation data caused by instrument replacement: Quantification based on pan evaporation observations. Journal of Geophysical Research-Atmosphere, doi: /2014JD023015
where Δ is the slope of the saturated vapor pressure at a given Ta (kPa/K), λ is the latent heat of vaporization of water (MJ/kg), γ is a psychometric constant (kPa/K), is the net radiative flux (MJ/(m2 d)), D is the vapor pressure deficit (kPa). a, b, c, and d were parameters, which were calibrated using the Bayesian approach proposed by Li et al. (2012).
Fig.3 Comparison of the calculated (CAL) and observed (OBS) monthly pan evaporation from the D20 pan
Fig.2 The Markov chains for the parameter estimations