HTML
-
(1) Satellite-based TRMM precipitation
The TRMM satellite is a remote sensing satellite jointly developed by the National Aeronautics and Space Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA). The precipitation radar (PR) sensor carried by TRMM, which is the world's first satellite-borne rain radar, can obtain quasi-global precipitation data with high temporal and spatial resolution (Huffman et al. [23]; Huffman et al. [24]). The TRMM 3B43 used in this study is a monthly precipitation product with a time resolution of one month and a time span from January 1998 to February 2019. The space coverage is global 50° S-50° N and the spatial resolution is 0.25° × 0.25°.
(2) MODIS Leaf Area Index (LAI) products
The Leaf Area Index (LAI), defined as half the total leaf area per unit ground surface area (Chen and Black [31]), can reflect the characteristics of regional plant growth and has been an important indicator in ecological and environmental changes. The Moderate Resolution Imaging Spectroradiometer (MODIS) Leaf Area Index (LAI) products (MOD15A2H) are the products with the longest time series and the best completeness so far. They are inversed based on a canopy radiation transfer model and a lookup table using MODIS daily surface reflectance products (MOD09), solar zenith angle, sensor observation angle, and land cover type (MOD12) (Knyazikhin et al. [32].) In this study, MOD15A2H with 8-day revisiting cycle and 500 m spatial resolution from 2000 to 2019 in Collection 6 is downloaded via the Earth Observing System Data and Information System (EOSDIS) of National Aeronautics and Space Administration (NASA) (https://earthdata.nasa.gov/). Monthly mean LAI is calculated with the products during each month from May to September, and they are further averaged to get the average values during vegetation growing season.
(3) Ground-based meteorological data
The variational processing method integrating remote sensing and ground observation is adopted in this paper to conduct variational correction of the TRMM satellite products. For this correction, we use ground rain gauge data from 2, 425 stations of the National Meteorological Information Center, China Meteorological Administration, with missing data and abnormal values eliminated.
The t2m data is from the"Dataset of monthly surface meteorological elements in China"released by the National Meteorological Information Center, China Meteorological Administration. The data of 2, 479 stations in the dataset from 1951 to 2013 underwent strict quality control in the development of ground basic meteorological data and in the production of datasets.
-
Aiming at overcoming the limitations of the observational data of ground stations and the precipitation products of TRMM satellite, this paper adopts the variational method to integrate the two kinds of data. Hence, the comprehensive variational correction processing technology, integrating the satellite remote sensing data and ground observation data, is used to modify TRMM satellite products (Xu [33]; Weng and Xu [34]). According to the variational principle, the functional equation depends on multiple independent variables.
$$ J[U(x,y)] = \iint _G {F\left( {x,y,U,\frac{{\partial U}}{{\partial x}},\frac{{\partial U}}{{\partial y}}} \right){\rm{d}}x{\rm{d}}y} $$ In this equation, U(x, y) must satisfy the following Euler equation:
$$ F u-\left(\frac{\partial}{\partial x} F u_{x}+\frac{\partial}{\partial y} F u_{y}\right)=0 $$ The precipitation field of the satellite data is set as R (x, y), and the corresponding rainfall gauge data field at the finite point is R(I, J). Then on the station coordinate (I, J), the difference field of the above two fields is the error field:
$$ C_{r}^{\sim}(I, J)=R(I, J)-R^{*}(I, J) $$ In fact, owing to the limited number of observation sites, it is necessary to construct a more generalized correction factor field function Cr (x, y) to meet the following conditions:
$$ \tilde{J}=\iint_{D}\left(C_{r}-C_{r}^{\sim}\right)^{2} \mathrm{~d} x\mathrm{~d} y \rightarrow \min $$ That is, $\sum\limits_{i} \sum\limits_{j}\left(C_{r}-C_{r}^{\sim}\right)^{2} $ reaches a minimum. A new factor field Cr (x, y) through variational correction is obtained, and the factor field after the variational revision is finally achieved:
$$ R(x, y)=R^{*}(x, y)+C_{r}(x, y) $$ This research program has achieved significant results in the objective correction of satellite remote sensing reanalysis on several aspects including satellite remote sensing retrieval of urban heat islands, the atmospheric element field in dust storm processes, and Threading Building Blocks (TBB) data under clear sky conditions (Cheng et al. [35]; Cheng et al. [36]; Bai et al. [37]).
-
To evaluate the performance of TRMM 3B43 products and the verified products, grid data are compared with ground rain gauge data using the nearest grid-to-point matching approach. Several statistical indicators are used to quantify the consistency between satellite precipitation and station data.
(1) Root mean square error (RMSE):
$$ {\rm{RMSE}} = \sqrt {\frac{1}{n}\sum_{i = 1}^n {{{\left( {{x_i} - {y_i}} \right)}^2}} } $$ where n is the total number of samples; xi and yi represent gauge observations and the corresponding values of the satellite, respectively. RMSE can be used to measure the deviation between the satellite precipitation and the observed data from the stations. The smaller the absolute value is, the closer the satellite precipitation is to the observed data.
(2) Correlation coefficient (r):
$$ r = \frac{{\sum\limits_{i = 1}^n {\left( {{x_i} - \bar x} \right)} \left( {{y_i} - \bar y} \right)}}{{\sqrt {\sum\limits_{i = 1}^n {{{\left( {{x_i} - \bar x} \right)}^2}} \sum\limits_{i = 1}^n {{{\left( {{y_i} - \bar y} \right)}^2}} } }} $$ The correlation coefficient is an exponential representing the degree of linear correlation between two variables. As for its absolute value, the closer to 1, the stronger the linear correlation between two groups of numbers will be. r greater than 0 represents positive correlation, while r less than 0 represents negative correlation.
(3) Excluding method
Excluding method is also adopted to further examine the ability of TRMM and verified TRMM precipitation products. To ensure sample independence during the testing, part of the station data are excluded before the revision. Since they are excluded in the correction, they can be compared with the original as well as the revised TRMM products independently.
-
The entire-layer water vapor flux (Q) is calculated using the following Equation:
$$ Q=-\frac{1}{\mathrm{~g}} \int_{P_{s}}^{P_{t}} q \vec{V} \mathrm{~d} p $$ Q can be divided into two directions:
$$ {qu(x, y, t) = - \frac{1}{{{\rm{g}}}}\int_{Ps}^{Pt} q (x, y, p, t)u(x, y, p, t){\rm{d}}p} $$ $$ {qv(x, y, t) = - \frac{1}{{{\rm{g}}}}\int_{Ps}^{Pt} q (x, y, p, t)v(x, y, p, t){\rm{d}}p} $$ where g is acceleration due to gravity, u/v is the zonal/meridional wind, q is specific humidity, Ps is the surface atmospheric pressure, Pt is the top atmospheric pressure and is set to be 300hPa, and qu and qv are the zonal and meridional water vapor fluxes, respectively.