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Regional Scale High Resolution δ18O Prediction in Precipitation Using MODIS EVI

  • Wei-Ping Chan ,

    Contributed equally to this work with: Wei-Ping Chan, Hsiao-Wei Yuan

    Affiliations Biodiversity Research Center, Academia Sinica, Taipei, Taiwan, School of Forestry and Resource Conservation, National Taiwan University, Taipei, Taiwan

  • Hsiao-Wei Yuan ,

    Contributed equally to this work with: Wei-Ping Chan, Hsiao-Wei Yuan

    Affiliation School of Forestry and Resource Conservation, National Taiwan University, Taipei, Taiwan

  • Cho-Ying Huang,

    Affiliation Department of Geography, National Taiwan University, Taipei, Taiwan

  • Chung-Ho Wang,

    Affiliation Institute of Earth Sciences, Academia Sinica, Taipei, Taiwan

  • Shou-De Lin,

    Affiliation Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

  • Yi-Chen Lo,

    Affiliation Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan

  • Bo-Wen Huang,

    Affiliation Taiwan Air Force Weather Wing, Taipei, Taiwan

  • Kent A. Hatch,

    Affiliation Biology Department, Charles William Post Campus of Long Island University, Brookville, New York, United States of America

  • Hau-Jie Shiu,

    Affiliation Department of Ecoscience and Ecotechnology, National University of Tainan, Tainan, Taiwan

  • Cheng-Feng You,

    Affiliation Department of Earth Science, National Cheng Kung University, Tainan, Taiwan

  • Yuan-Mou Chang , (SFS); (YMC)

    Affiliation Department of Ecoscience and Ecotechnology, National University of Tainan, Tainan, Taiwan

  • Sheng-Feng Shen (SFS); (YMC)

    Affiliation Biodiversity Research Center, Academia Sinica, Taipei, Taiwan

Regional Scale High Resolution δ18O Prediction in Precipitation Using MODIS EVI

  • Wei-Ping Chan, 
  • Hsiao-Wei Yuan, 
  • Cho-Ying Huang, 
  • Chung-Ho Wang, 
  • Shou-De Lin, 
  • Yi-Chen Lo, 
  • Bo-Wen Huang, 
  • Kent A. Hatch, 
  • Hau-Jie Shiu, 
  • Cheng-Feng You


The natural variation in stable water isotope ratio data, also known as water isoscape, is a spatiotemporal fingerprint and a powerful natural tracer that has been widely applied in disciplines as diverse as hydrology, paleoclimatology, ecology and forensic investigation. Although much effort has been devoted to developing a predictive water isoscape model, it remains a central challenge for scientists to generate high accuracy, fine scale spatiotemporal water isoscape prediction. Here we develop a novel approach of using the MODIS-EVI (the Moderate Resolution Imagining Spectroradiometer-Enhanced Vegetation Index), to predict δ18O in precipitation at the regional scale. Using a structural equation model, we show that the EVI and precipitated δ18O are highly correlated and thus the EVI is a good predictor of precipitated δ18O. We then test the predictability of our EVI-δ18O model and demonstrate that our approach can provide high accuracy with fine spatial (250×250 m) and temporal (16 days) scale δ18O predictions (annual and monthly predictabilities [r] are 0.96 and 0.80, respectively). We conclude the merging of the EVI and δ18O in precipitation can greatly extend the spatial and temporal data availability and thus enhance the applicability for both the EVI and water isoscape.


The water isoscape, the natural variation in stable water isotope ratios [1], [2], has been an important tool in disciplines as diverse as hydrology [1], [3], paleoclimatology [2], ecology [4] and forensic investigation [5]. However, the major limitation of applying isotopic technology is the low density and poor continuity of spatial datasets over multiple year time scales [6]. An important approach to resolve this limitation is to develop space-time-explicit predictive models of water isotope distributions [7], [8]. Existing water isoscape models are almost all based on modeling hydrological cycles, which have greatly enhanced our understanding of isotopic physics and help in predicting large-scale water isoscapes [9], [10]. Nevertheless, complex hydrological processes, such as water transport, exchange, and cloud process, almost inevitably decrease the predictability of these models. Thus, these complexities limit application of the hydrological modeling approach to generate water isoscape values at high accuracy and fine scales [11]. The critical challenge of improving predictability of an isoscape model remains the central focus for isotopic research.

Here, we develop a novel approach to predict the precipitated water isoscape. Instead of modeling the hydrological cycle, we used the Enhanced Vegetation Index (EVI), which is a remotely sensed data product of the Moderate Resolution Imagining Spectroradiometer (MODIS) on board the National Aeronautics and Space Administration’s (NASA’s) Terra satellite (MOD13Q1), to estimate the precipitated water isoscape with high spatial and temporal accuracy. The EVI is also an important multidisciplinary tool and can be a surrogate for plant growth [12] or its related biophyscial attribuets such as leaf area index (LAI) [13] in areas with minimum amount of snow cover through time; it is designed for monitoring a wide range of vegetation types (e.g., coniferous and broadleaved/deciduous and evergreen forests) at the global scale [13], which are highly affected by climatic regimes and topography. Similarly, it has also been well-known that the precipitated water isoscape is also influenced by these same factors [14] (Fig. 1). Thus, we propose to link these two well-established, but previously separated fields. This novel approach will enable us to predict precipitated δ18O (referred as δ18O hereafter, see Materials and Methods for details) by using the easy-access EVI data without explicit knowledge of various climatic and topographic data needed by previous isotopic models.

Figure 1. The conceptual basis of merging the EVI and δ18O.

The direction of influence of each factor is represented by the arrows. Functions that are directly influenced by spatial and climatic factors are listed in the parentheses within the EVI and δ18O boxes. “A” is the constraint of spatial extent for EVI data, where is restricted by the amount of snow cover. “B” is the description of the characteristics of output (δ18O) including high resolution, large spatial scale, and various temporal scales (16-day, monthly, seasonal or yearly estimation). “C” is the limitation of δ18O data. It should be monthly data or the model should be modified to a different temporal scale. “D” indicates the long temporal extent of output of the EVI data. Only temperature, precipitation, and altitude are included in our SEM analysis but other topographic and climatic factors may also be included. References for each relationship is as follows (These references are listed in Text S1): [3][7],[1], [8][10],[2], [9], [11],[3], [8], [10], [12],[5], [13][17],[18][20],[6], [21], [22],[13], [15], [22],[23][25].

In addition to the predictive model, we also used the structural equation model (SEM), which includes factor analysis, path analysis and regression [15], to explore how climatic and topographic factors influence the integrated EVI (the iEVI, the growing season integrated EVI, measured as the area under the EVI series.) and precipitated δ18O through time.

Materials and Methods

A. Data Collection

The water samples were collected along an elevational transect in the central Taiwan, from Taroko to Wulin (22°–24°N, 120°–122°E, Fig. 2) by the precipitation collected facility (PCF) [16] approximately once a month from April 2007 to December 2009. The data were collected at Lishan [17] (crop land, 121°15′1.5″E, 24°15′32.83″N, 1684 m a.s.l.) is from June, 2003 to May, 2004 and Piluchi (forest, 121°18′28.49″E, 24°13′34.02″N, 2363 m a.s.l.) is from December, 2008 to November, 2009). To prevent the effect caused by the heavy rainfalls mainly induced by tropical cyclones, we collected the water sample right before and after the events. The PCF was composed by a dark glass bottle (1500 c.c.) with 2 cm high mineral oil inside to block the evaporation of collected water, and a plastic funnel (diameter is 6 cm) at the top of the bottle with lace curtain covered to avoid litters. The PCFs were tied at the open area, which have no cover above the funnel [16]. The amounts of samples were first measured in a cylinder (500 c.c.) and recorded as amount of precipitation. We stored samples in a 4°C freezer until analyzing.

Figure 2. The precipitation collection site.

Thirteen precipitation collection sites along an elevation gradient in the eastern Taiwan.

Water samples were treated by using CO2-H2O balancing method [18] and Zinc reduction method [19] and measured in a VG SIRA 10 isotope ratio mass spectrometer to obtain δ18O value and δD value [20] (Fig. S1).

The EVI data was derived from MODIS observations, produced every 16 days, and downloaded from the NASA website from 2006 to 2010. The hourly temperature data was collected along the elevation transect by the weather stations, which were located in Fushi (109 m), Tiansiang (550 m), Lishan (1980 m), Dayuling (2365 m), Hehuan Mountain (3292 m).

B. Data Preprocessing

Isotopes measurements and the amount of precipitation occurred in the same temporal scale. The 16-day EVI values (23 sets of data per year) were extracted using ENVI v. 4.6.1 (ITT Visual Information Solutions, Boulder, Colorado, USA). Each site has 23 values a year. Including each value at the middle of the 16 days, and using the “Savitzky-Golay Spline Estimation” function of TIMESAT [21], where the number of envelope iteration was 3, the Adaption Strength is 3, the Savitzky-Golay window size was 5 and the season end is 0.167 (1/6). The iEVI is the growing season integrated EVI, measured as the area under the EVI series, starting from the one sixth of the growing season to the end of the growing season (Fig. S2, For the iEVI calculation, see also Mendez-Barroso et al.(2009) [22]). In addition, extrema in the data would cause highly uncertainties in prediction along temporal dimensions, so we excluded extrema in the data when comparing predictability (<1 data per season was excluded). Finally, we integrated the EVI to the same temporal scale as δ18O data. The quadratic formula prediction was obtained by using Wolfram Mathematica 8 [23]. All data with variances are presented as means ± standard error.

C. To Obtain the Optimal EVI-δ18O Function

Our data is predicted by Wolfram Mathematica 8 with the function:and analyzed in SPSS 18. The sample code of the function to obtain the parameters of the iEVI-δ18O function is proved below.


 evidatan = 20;

 times = 30;


  For[j = 1, j < =  evidatan, j++, {

   singleresult =  ConstantArray[0, {times, 7}];

   result  =  ConstantArray[0, 63];

   t = 1;

   fit  =  ConstantArray[0, evidatan];

   inputxx  =  Import[“c:/users/……/data.xls”][[1, All, j]];

   inputyy  =  Import[“c:/users/……/data.xls”][[1, All, evidatan + j]];

   inputx  =  Drop[inputxx, -Count[inputxx, “na”]];

   inputy  =  Drop[inputyy, -Count[inputyy, “na”]];

   data  =  ConstantArray[0, Length[inputx]];




     For[k = 1, k < =  times, k++, {

      For[i = 1, i < =  Length[inputx], i++, data  =  ReplacePart[

       data, {i} −> {inputx[[i]], inputy[[i]]}]];

      model  =  −a (Abs[x - b] + c)2+ d x - e;

      Remove[a, b, c, d, e];

      fit  =  FindFit[

       data, {model, {ca < a, 20< b <300, −200< c <0,

        cdmin < d < cdmax, 0< e <100}}, {a, b, c, d, e}, x];

      rr  =  {a, b, c, d, e}/. fit;

      rcy  =  ConstantArray[0, Length[inputx]];

      For[m  = 1, m < =  Length[inputx], m++,

       {xx  =  Extract[inputx, {m}],

        rcy  =  ReplacePart[rcy,

         m −> −rr[[1]] (Abs[xx - rr[[2]]] + rr[[3]])2+

          rr[[4]] xx - rr[[5]]]}];

      rms  =  Sqrt[Accumulate[(rcy - inputy)2][[Length[inputx]]]];

      singleresult  =  ReplacePart[singleresult, k -> {rr[[1]], rr[[2]], rr[[3]], rr[[4]], rr[[5]], Correlation[rcy, inputy]2, rms}];


      result  = 

       ReplacePart[result, t -> SortBy[singleresult, Last][[1]]];

      t  =  t +1;

      }, {cdmax, 0.1, 0.3, 0.1}]

     }, {cdmin, −0.1, −0.3, −0.1}]

    }, {ca, 0.0005, 0.0035, 0.0005}]

   Print[SortBy[result, Last][[1]]];




Where the factor range need to be limited. a>0.0005, 20<b<300, −200<c<0, −0.4<d<0.4, 0<e<100. The data.xls format need to be:

E(i, j) E(i+1, j)……O(k, j) O(k+1, j).

E(I, j+1) E(i+1, j+1)……O(k, j+1) O(k+1, j+1).

E(I, j+2) E(i+1, j+2)……O(k, j+2) O(k+1, j+2).

If the length of the data lines are not the same, use “na” to fill all the blank area of the data to make sure all data lines are same length. The parameter “evidatan” required the number of lines (k-1) of the EVI data, and the parameter “times” required the times that Mathematica to find the fitted parameter value. We suggest 30 as the optimal number.

D. To Make Predictions by the EVI-δ18O Function

The code to obtain the parameters of the iEVI-δ18O formula is provided below.

evidatan  =  Length[Import[“c:/users/……/constant.xls”][[1, All, 1]]];

For[j  = 1, j < =  evidatan, j++, {

 fit  =  ConstantArray[0, eendline];

 inputxxx  =  Import[“c:/users/……/data.xls””][[1, All, j]];

 inputxx  =  Drop[inputxxx, -Count[inputxxx, “na”]];

 constant  =  Import[“c:/users/……/constant.xls ”][[1, j, All]];

 rcy  =  ConstantArray[0, Length[inputxx]];

 For[m = 1, m < =  Length[inputxx], m++, {xx  =  Extract[inputxx, {m}],

  rcy  =  ReplacePart[rcy, m −> -constant[[1]] (Abs[xx - constant[[2]]] + constant[[3]])2+ constant[[4]] xx - constant[[5]]]}];


  The format of data.xls is just as the description above. The format of constant.xls is:

Where n is equal to the “evidatan”, the number of lines (k-1) of the EVI data. It is important that all of the blank areas of the table are count as {} in Mathematica 8. Consequently, to remove all these blanks is crucial. The value of the parameter b of any given time needs to be adjusted by the following formula:

bpredict = (bmodel/iEVIcomplete growing season of model)* iEVIcomplete growing season of prediction.

Where bpredict represents the parameter b, which needs to be input in prediction model, bmodel represents the most fitted value of parameter b (output from Mathematica) when building the model, the iEVIcomplete growing season of model represent the data used to construct the model and the iEVIcomplete growing season of prediction represent the iEVI in the growing season needs to be predicted.

E. The Stability of the EVI and δ18O

In natural settings, the stabilities of temporal EVI and δ18O are depicted as the standard deviation of the four-year time-series EVI and δ18O data, respectively. Throughout the result section, p represents the probability of obtaining a test statistic at least as extreme as the one that was actually observed and r represents correlation coefficient, which provides the strength and direction of the dependency between two sets of data.


A. The Relationship among Climatic, Topographic Factors, the iEVI and δ18O

Using water samples for δ18O analysis collected from 13 sites along the elevation gradient (91–2876 m above sea level [a.s.l.]) in central Taiwan from April 2007 to September 2009 (Fig. 2), we found that the spatiotemporal pattern of δ18O was highly correlated with the iEVI. Our SEM analysis (n = 403) showed that the effects of precipitation and temperature were pronounced (p<0.001) for both the iEVI (r = 0.18 and 0.7, respectively) and δ18O (r = −0.68 and −0.34, respectively) (Fig. 3a). Furthermore, 91% and 88% (p<0.001) of the iEVI and precipitated δ18O can be explained by the climatic and topographic factors, respectively. Additionally, the parts of the iEVI and δ18O that were not explained by precipitation, temperature, time and elevation were also highly correlated (r = −0.53, p<0.001, Fig. 3a). Using the same analysis but substituting the climatic factors with the iEVI, the δ18O can still explain 88% of variation (Fig. 3b, p<0.001, n = 403). Moreover, there is a positive linear relationship between the variability of temporal EVI and δ18O (r = 0.9, p<0.001, Materials and methods E, Fig. S3). Therefore, the results suggest that the iEVI should be a significant variable for predicting δ18O.

Figure 3. SEM analysis of the relationship among climatic, topographic factors, the iEVI and δ18O.

a, The relationships among the iEVI and δ18O and other climatic, topographic factors. The “Err” circles represent the parts that were not explained by above factors in both the iEVI and δ18O, but can be explained by each other. b, The relationship between topographic factors, the iEVI and δ18O (the climatic factors are replaced by the iEVI). All values are under two tailed t-test, and are significant (p<0.001). The values shown here are correlation coefficients (r), unless noted as r2 representing the overall variability explained by other factors that connect to the box.

B. Using the iEVI to predict δ18O

We further developed a predictive function of using iEVI to predict δ18O (referred as iEVI-δ18O function, hereafter):where a, b, c, d and e are constants and vary in different sites, Table 1). Thus, even EVI values are the same among different sites at a given time period, the predicted δ18O values might still be different since their iEVI-δ18O functions are different. We provide a standard procedure of using this function and data from a single growing season to find the predictive function (i.e. find different constants) in each site (Fig. S4 for the summary of model construction). As a consequence, we can predict continuous time-explicit (every 16 days) δ18O values for other seasons in the same region at a spatial resolution of 250 m.

C. Predictability of the iEVI-δ18O Functions

We used the δ18O data collected in Taiwan with the iEVI data in 2007 to develop the iEVI-δ18O functions (only four pairs of the iEVI-δ18O data were used, one was in the beginning, two were in the middle, and one was at the end of a given growing season) and used the iEVI data to predict δ18O in 2008 and 2009. We then utilized this function to predict annual or seasonal δ18O for different year(s). By replicating this method, we then cross-validated our models also yielding high (p<0.001) annual (r = 0.96), seasonal (r = 0.96) and monthly (r = 0.80±0.17) predictabilities (Table S1). High predictabilities (r ≥ 0.84) were also observed in other land cover types such as crop land and forest (Materials and methods A).

The iEVI-δ18O functions can provide not only accurate annual/monthly δ18O as described above, but within year δ18O estimate. The iEVI-δ18O functions were developed using only four-pairs of the iEVI-δ18O data to predict the within-season monthly δ18O value, and the model was robust (r = 0.95±0.01, p<0.001, Table S1). Note that the predictability of models was slightly weakened (r ≥ 0.54, p<0.001) during the summer monsoon season (July-September) mainly due to episodic heavy rainfalls presumably induced by tropical cyclones.

For finer scale spatial δ18O estimation, we found that the predictability of the iEVI-δ18O functions was significantly higher when using focal EVI values compared to using EVI values in surrounding grids (mean difference in predictability [r] for using focal grids and (1) grids 250 meter away [56 grids]: −0.0098±0.00305, p = 0.002, and (2) grids 500 meters away [112 grids]: −0.0070±0.00229, p = 0.003). This justified the use of MODIS EVI for high resolution mapping of δ18O. Given the high spatial predictability of our functions, we can use a single season’s data set for three elevations (91, 1676 and 2876 m a.s.l.) to interpolate the δ18O of other sites with high accuracy (p<0.001) along the elevation gradient at the regional scale (annual prediction with r = 0.96 and monthly prediction with r = 0.77±0.00, Figs. 3 and S5, S6). Thus, we can use the iEVI-δ18O relationship and the δ18O-topography relationship to generate a detailed regional scale (250 m×250 m) δ18O isoscape (Fig. 4).

Figure 4. The fine scale regional δ18O prediction map of Taiwan in August, 2009.

The inset highlights the fine resolution (250 m) of modeled result.

Figure 5. The fine spatiotemporal scale predictability of the model.

The predictability in continuous elevation and time data is shown. Using one-growing-season the iEVI-δ18O function at Taroko (91 m a.s.l.), Sinbaiyang (1676 m) and Siafongkuo (2876 m) and the δ18O-altitude relationship to predict the δ18O values along the elevation gradient and in other growing seasons.


Since the EVI is available at the global scale with 16-day sampling intervals, our approach in using the EVI to predict the water isoscape can potentially increase the accessibility of water isotope data in both spatial and temporal dimensions. The previously developed models are especially useful in improving our climatological understanding of isotope distributions at the global scale [24], [25]. Most of these existing models can also be applied to provide long-term averaged climatological predictions at the monthly or seasonal time scales at high spatial (km or sub-km) resolutions where appropriate gridded input data are available. However, small scale hydrological phenomena could not be easily integrated into the global model [26], [27] and, similarly, taking local topographic attributes into account is computationally costly for predicting the global water isoscape [11]. These limitations might be the reasons that existing models have not been applied to finer spatial and temporal scale predictions.

To our best knowledge, our model is the first model providing high accuracy spatial predictions along different altitudes at monthly (calendar month) time scale (Fig. 5). In addition, our model also produced higher resolution (250 m×250 m) water isoscape predictions and accuracy than all the existing models in all temporal scales. Therefore, we believe the proposed approach can further enhance the application of the water isotope data and analyses, especially in cases where fine scale and high accuracy isoscape data are important, such as in hydrology [1], [3], forensic investigations [5] and animal migration research [28]. Different from the existing isoscape models that are based on modeling the hydrological cycle, our model can obtain better prediction with minimal efforts of precipitated δ18O sampling.

Discovery of a strong relationship between the EVI and δ18O also permits potential research directions. For instance, the EVI is only available since year 2000 and thus mainly limited by its temporal extent. However, water isotope data from the past can be recovered in some areas from various sources, such as tree rings [29] and sediments [2]. By building the EVI-δ18O function and obtaining historical water isotope data, we could retrieve the paleo-EVI information. Since the time-series EVI can be an indicator for NPP [22], [30], we can then investigate the influences of paleoclimte on ecosystem productivity.

This study demonstrates that the EVI and water isotope data can compensate for each other and extend their applicability. The proposed approach can currently be applied to any terrestrial site with four precipitated δ18O data in a season. However, due to lacking of the isotopic data worldwide, the continental and global scale EVI-δ18O functions, such as incorporating latitudinal effects in different climate zones, cannot yet be achieved.. Therefore, our study highlights the importance of maintaining a comprehensive global isotope data network, such as improving the Global Network of Isotopes in Precipitation (GNIP), which facilitates constructing global water isoscapes at great detail.

Supporting Information

Figure S1.

A local meteoric water line (b) (with corresponding residuals [a]) in the mountainous region of Taiwan.


Figure S2.

Illustration of the integrated EVI. The arrows point to the beginning and the end of a growing season depicted by the EVI time-series data. The shaded area is an example of the iEVI.


Figure S3.

Variablity of the EVI and δ18O. The linear positive correlation between the variability of the EVI and the stability of δ18O. Only data from sites in natural forests were shown to demonstrate the relationship in nature habitats. However, the result is qualitatively the same if all sites were included.


Figure S4.

Summary of the prediction model construction process. Yellow, blue and white boxes represent raw data needed for constructing the prediction model, procedures of building models, and predicted targets, respectively (i.e. Ingesting the iEVI of specific time and location in the model can predict δ18O and vice versa).


Figure S5.

A scatter plot of monthly predictions. Monthly δ18O predictions vs. observations in regional scales.


Figure S6.

Predictabilities of the model across the elevation gradient. Dots represent the mean predictabilities across an elevation gradient with standard errors (bars).


Table S1.

The integrated predictabilities ( r ±SEM [if shown]) under different initial conditions.



We greatly appreciate S. Ustin, I.C. Chen and G. Bowen for helpful comments on early versions of the manuscript and the advice and support of K.T. Chen and the members of Lab of Wildlife Animals at National Taiwan University. We thank K. H. Chien, J.H. Shen and H.C. Wang for helping on early analysis of the remote sensing data, X.L. Wei and J.H. Chen for helping the field work, and J.C. Lin, A.Y. Zhang and S.I. Yu for preprocessing the climatic data and early computation. We thank D. Tingey for assistance with the isotope analyses. Finally, we also thank the more than 20 volunteers for their help in the field and lab.

Author Contributions

Conceived and designed the experiments: WPC SFS HWY YMC. Performed the experiments: WPC YMC HJS. Analyzed the data: WPC SFS CYH SDL YCL. Contributed reagents/materials/analysis tools: CHW KAH CFY BWH. Wrote the paper: WPC SFS HWY YMC CYH. Developed the isotopic models and interpreted the data: WPC SFS. Analyzed the EVI data and did the computation of remote sensed data: WPC CYH.


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