A Statistical Method for Recovering the Depth A Statistical Method for Recovering the Depth to Shallow Groundwater Table in Chinato Shallow Groundwater Table in China

袁 星袁 星谢正辉，梁妙玲谢正辉，梁妙玲

中国科学院大气物理研究所中国科学院大气物理研究所xyuan@mail.iap.ac.cnxyuan@mail.iap.ac.cn

2006.08.102006.08.10

BackgroundBackground DataData MethodologyMethodology Validation & ApplicationValidation & Application SummarySummary

在全球总水量中，海洋占 97% 以上，偏远而难以利用的两极冰帽及冰川约占 2% ，其余不到 1% 才是人类可取用的水资源，而其中地下水的储存总量居冠。地下水的过量开采会造成地下水位的大幅下降，引起地面沉降。地下水位过高会对农作物生长不利，造成渍害。因此，研究地下水位的动态对国计民生具有重大意义。

Groundwater

气候条件、植被地形和人类活动的变化能引起地下水埋深时空分布的变化；反之，大尺度地下水埋深的变化，导致土壤含水量、地表径流和基流的改变，进一步影响下垫面的蒸散发和低层大气感热和潜热的分配，从而对气候产生影响。

估计浅层地下水埋深变化对水资源研究、陆面过程模拟、陆地生态系统及陆气相互作用的研究具有重要意义。

Transfer function-noise (TFN) models & parameter transfer method.

Purpose

To recover monthly data for the depth to shallow groundwater table since 1961 in continental China.

Scheme

DataMeteorological Data (1961-2000)Daily time-series of precipitation, maximum temperature, and minimum temperature are obtained by interpolating station values from 740 meteorological stations in China.

Soil DataThe soil texture information is derived from Food and Agriculture Organization dataset (FAO).

GroundwaterPhreatic data from monitor wells.

Locations of the meteorological stations

Locations of wells interpolated into 60×60 km2 grids

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Methodology :Ⅰ

Calibration

TFN model

Input:

precipitation surplus (precipitation minus potential evapotranspiration).

The instantaneous evaporative demand (mm/s) is calculated following Jarvis and McNaughton (1986):

ns Rs

pet

2 ( sin( ))sk uu hn vv hns

dpet

*t t tG G n

* *1t t tG G P

1( ) ( )t t tn c n c a

TFN model

* *1 01

1 11

0 0 0

0 0 (1 ) 1 1tt t

t

t t

PG Ga

cn n

State-space representation

A linear discrete stochastic system

t t t tY C X

1t t t tX AX BU Da

State equation

Measurement equation

If no observation taken at time t

If there is an observation at time t

ˆt tX X

t tM

t t t tv y C X 2 2,

Tv t tCM C

2 1,{ }T

t t v tK M C ˆt t t tX X K v ( )t t tK C M

1 1 1ˆ

t t t tX AX BU BU 2

1T T

t t aM AP A D D

Recursive application of the Kalman filter

2( , , , , )ac Tα

Running the Kalman filter for the calibration period

with a parameter set

resulting in the following objective function:

22, 2

1 1 ,

( )( ; ) ln(2 ) ln( ( )) ( )

( )

N Ni

v ii i v i

vJ N N

Using SCE-UA (shuffled complex evolution method developed at The University of Arizona) method to minimize the objective function.

Identification of TFN modelTransform data to improve normality and stationarity,

and determine parameters which will be calibrated.

Representation of TFN model invector notations(state space form)

Generate sampleSample s points randomly in the feasible parameter space.

Running Kalman filter for Optimal prediction

(calculate the criterion values)

Rank pointsSort the s points in order of increasing criterion value.

Partition and evolvePartition the s points into p complexes,evolve each complex

Shuffle complexesCombine the points into a single sample population.

convergence criteriasatisfied?

Yes

Output calibrated parameters

No

Flow chart: the calibration method of TFN model

Methodology :Ⅱ

Parameter Transfer

1 Tropical climate 2 Dry, cold climate

3 Rainy, midlatitude climate 4 Continental climate with hot summer

5 Continental climate with cool summer

6 Continental climate with short cool summer

聚类 (clustering)

基于平方误差的聚类 K 均值 (K-Mean)

基于概率密度估计的聚类 高斯混合模型： GMM 核密度估计： mean-shift

层次聚类 基于图的聚类 模糊聚类 基于神经元网络的聚类

高斯混合模型 (GMM)(Mixture of Gaussians Model)

基本思想：将聚类视为一个概率密度估计问题 给定一堆多峰分布的数据，估计其概率密度

Expectation-Maximum likelihood (EM) Algorithm

EM Algorithm

Validation of TFN models

Mean Absolute Error: 0.18m 0.15m 0.19m 0.15m

Estimation and 95% confidence intervals of the depth to groundwater table for the four grids

Autoregressive parameter of transfer model

Moving average parameter of transfer model

Autoregressive parameter of noise model

Variance of noise series

Cross Validation

Time series of errors for cross validation.

(a) ME(t); (b) RMSE(t); (c) MAE(t)

r=0.003

r=0.357 r=0.293

Transfer function-noise (TFN) models are calibrated by SCE-UA method coupled with Kalman filter in each observed grids.

Parameters for gauged grids are transferred to ungauged grids by GMM clustering method based on soil property data and 40-years meteorologic data such as precipitation and temperature.

The depth to groundwater table for continental China are estimated by the TFN models with parameters calibrated or transferred.

Reconstruction Scheme

(1) Validated by phreatic data, TFN models not only provide results with high accuracy, but also can quantify the prediction uncertainty reasonably well.(2) Cross validation shows that the parameter transfer scheme is an effective way for the recovery.(3) The seasonal variations of recharge and discharge for groundwater in China are obtained by our scheme.(4) The second EOF match the pattern of mean depth of the groundwater reasonably well.

Conclusions

Future work

Further validation and modification of our data by satellite data such as GRACE.

Assessing the improvement of Land surface model or climate model, running with initial conditions provided by the recovered data.

谢谢指导！Thank You!