role of meteorological controls on interannual variations ... · research article...

RESEARCH ARTICLE10.1002/2015WR018493

Role of meteorological controls on interannual variations inwet-period characteristics of wetlandsYanlan Liu1 and Mukesh Kumar1

1Nicholas School of the Environment, Duke University, Durham, North Carolina, USA

Abstract Many ecological functions of wetlands are influenced by wet-periods, i.e., the time intervalwhen groundwater table (GWT) is continuously near the land surface. Hence, there is a crucial need tounderstand the controls on interannual variations of wet-periods. Given the scarcity of long-term measure-ments of GWT in wetlands, understanding variations in wet-periods using a measurement approach alone ischallenging. Here we used a physically based, fully distributed hydrologic model, in synergy with publiclyavailable hydrologic data, to simulate long-term wet-period variations in 10 inland forested wetlands in asoutheastern US watershed. A Bayesian regression and variable selection framework was then implementedto (a) evaluate the extent to which the simulated wet-periods can be estimated and predicted by precipita-tion (Ppt) and potential evapotranspiration (PET) and (b) infer the relative roles of seasonal Ppt and PET. Ourresults indicate that wet-period start date and duration could vary by more than 6 months during the 32year simulation period. Remarkably, 60–90% of these variations could be captured using regressions basedon seasonal Ppt and PET in most wetlands. Effects of seasonal meteorological conditions on wet-period var-iations were found to be nonuniform, which indicate that the annual variables may not explain interannualvariations in wet-periods. The Bayesian framework was able to predict wet-period variations with errorssmaller than 1 month at a 90% confidence level. The presented framework provides a minimalistic approachfor estimating and predicting wet-period variations in wetlands and may be used to understand the futureresponses of associated ecological functions in wetlands.

1. Introduction

Wetlands have recently drawn increased attention in ecosystem science and management because of theirstrong influence on carbon and nitrogen cycles, water quality, and biodiversity. It is estimated that 18–30%of total global soil carbon is stored in wetlands despite them covering only 6–7% of the land area [Lehnerand D€oll, 2004]. CH4 emissions from wetlands constitute a significant component of the global CH4 budget,accounting for 20–40% of the total CH4 emissions [Denman, 2007; Bousquet et al., 2006; Ciais et al., 2014].Wetlands also act as nitrogen sinks and help buffer nutrient contamination of streams [Brinson et al., 1984;Hefting et al., 2004; Vidon and Hill, 2004]. One of the key controls on the aforementioned ecohydrologicalfunctions of wetlands is the groundwater table (GWT). GWT variations have been observed to influence thegreenhouse gas emissions from wetlands [Moore and Roulet, 1993; Nyk€anen et al., 1998; Walter et al., 2001;Chimner and Cooper, 2003; Strack et al., 2004; Bohn et al., 2007; Jungkunst and Fiedler, 2007; Turetsky et al.,2008; Zona et al., 2009; Bloom et al., 2010; Miao et al., 2013; Sch€afer et al., 2014]. Nitrogen cycling processessuch as nitrification, denitrification, and ammonification, which are triggered by the anoxic conditions inwetland soil, are also known to be strongly influenced by GWT variations [Regina et al., 1996; Hefting et al.,2004; Rodriguez-Iturbe et al., 2007; Schilling, 2007; Lohila et al., 2010; Goldberg et al., 2010]. Several studieshave also highlighted the role of GWT in influencing the vegetation distribution [Schilling, 2007; Todd et al.,2010], vegetation community competition [Sch€afer et al., 2014], and transpiration and biomass dynamics[Patten et al., 2008] in wetlands. In this context, a GWT height of 20.3 m (negative sign indicates GWT depthbelow the land surface datum) is often considered as a critical threshold that influences the eco-hydrological functions of wetlands. For example, observed CH4 emissions (Figure 1) compiled from multiplewetlands situated in climatically diverse settings [Moore and Knowles, 1989; Moore and Dalva, 1993; Shannonand White, 1994; MacDonald et al., 1998; Strack et al., 2004; Jungkunst and Fiedler, 2007; Turetsky et al., 2008]show that CH4 emissions were significantly larger (P< 0.001) when the GWT was higher than 20.3 m.Hefting et al. [2004] indicated that ammonification and denitrification mainly occurred when GWT was

Key Points:! 60–90% of interannual variations in

wet-period can be explained byseasonal Ppt and PET! Impacts of seasonal Ppt and PET on

wet-period variations are nonuniform! The presented Bayesian framework

predicts the wet-period variationswith small errors

Supporting Information:! Supporting Information S1! Supporting Information S2

Correspondence to:M. Kumar,[email protected]

Citation:Liu, Y., and M. Kumar (2016), Role ofmeteorological controls on interannualvariations in wet-period characteristicsof wetlands, Water Resour. Res., 52,doi:10.1002/2015WR018493.

Received 18 DEC 2015Accepted 31 MAY 2016Accepted article online 6 JUN 2016

VC 2016. American Geophysical Union.All Rights Reserved.

LIU AND KUMAR METEOROLOGICAL CONTROLS ON WET-PERIOD 1

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higher than 20.3 m while nitrificationoccurred when GWT was lower than20.3 m in a riverine wetland. Averageroot zone depth of many wetland veg-etation species is also around 0.3 m[Lieffers and Rothwell, 1987; Sj€ors, 1991;Lewis, 1995]; hence, the threshold islikely to influence many wetland vege-tation functions by controlling aerobic/anoxic conditions in the root zone. Thesignificance of the 20.3 m threshold isalso obvious from its use as one of thecriteria for wetland delineation by USNational Research Council [Lewis,1995]. These studies indicate that forbetter understanding and predictionof carbon and nitrogen cycle and veg-etation functions in wetlands, it is cru-

cial to first evaluate wet-periods, i.e., the duration for which GWT is higher than 20.3 m in wetlands.

This study focuses on evaluating interannual variations in start date and duration of wet-periods in 10inland forested wetlands located in a southeastern US watershed. Although temporal variations in GWT aremediated by a number of factors including microtopography [Frei et al., 2010; Moffett et al., 2010], landscapedrainage network [Todd et al., 2006], land use [Batelaan et al., 2003], soil properties [Vidon and Hill, 2004],and vegetation [Baird and Maddock, 2005; McCarthy, 2006], these variations are known to be primarilydriven by meteorological conditions [Changnon et al., 1988; Reich et al., 2002; von Asmuth and Knotters,2004; Yu et al., 2015] in inland wetlands. As such, we also explore the role of meteorological conditions oninterannual variations in wet-period characteristics.

Given that observing GWT is time and effort-consuming, a majority of the studies on wetland GWT dynam-ics have focused on measurements spanning a few months or years [Devito et al., 1996; Rosenberry andWinter, 1997; Ferone and Devito, 2004; Wolski and Savenije, 2006; Todd et al., 2006; Kaplan et al., 2010; Caoet al., 2012]. Clearly, the lack of long-term measurements of GWT in wetlands, especially in the southeasternUS, poses a challenge for studying interannual variations in wet-period characteristics using a measurementapproach alone. Moreover, considering that most of the measurements were usually confined to areaswithin or close to a single wetland, the studied GWT dynamics may be site-specific and not representativeof the GWT response in other nearby wetlands. To circumvent these challenges, here we use a distributedintegrated hydrologic model, in synergy with publicly available hydrologic data, to simulate long-term GWTdynamics in multiple wetlands within a southeastern US watershed. The simulated GWT in wetlands arethen analyzed using a Bayesian regression approach to answer four specific questions: (1) What is the rangeof interannual variations in wet-periods? (2) To what extent can annual and seasonal meteorological condi-tions explain interannual variations in wet-periods, and do antecedent conditions also impact wet-periodvariations? (3) What is the relative seasonal influence of meteorological conditions on wet-period variations?and (4) How well can the interannual wet-period variations be predicted using seasonal meteorological con-ditions? To address these questions, the paper is organized as follows. Section 2 describes the implementa-tion, calibration, and validation of a hydrologic model; a framework for Bayesian regression and variableselection; and the experiment details. Section 3 discusses the results by organizing them in four subsec-tions, each corresponding to the four questions outlined above. Section 4 summarizes the main conclusionsof the study and discusses implications for future research.

2. Data and Methods

2.1. Study SiteThe study was conducted in a southeastern US watershed (area 5 325 km2) that drains into Second Creeknear Barber, North Carolina (35.68N, 80.78, USGS streamflow gage 02120780). The watershed was selected

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1 Moore and Knowles, 1989Moore and Dalva, 1993Shannon and White, 1994MacDonald et al., 1998Strack et al., 2004Jungkunst and Fiedler, 2007Turetsky et al., 2008

Figure 1. Relation between CH4 fluxes and GWT in wetlands. To account fordifferent magnitudes of CH4 emissions from different wetlands, the data wascompiled by normalizing the CH4 flux rates within each wetland into a [0,1]interval, following Jungkunst and Fiedler [2007]. Blue and green points representthe observations with GWT above and below 20.3 m, respectively.

Water Resources Research 10.1002/2015WR018493


because it contains multiple forested freshwater wetlands within its boundary. The forested wetlands arewidespread across the southeastern US and account for more than 35% of the total forested wetland areain the continental US [Bridgham et al., 2006]. These wetlands are known to provide several ecological func-tions including carbon sequestration and greenhouse gas emissions [Schipper and Reddy, 1994; Roden andWetzel, 1996; Bridgham et al., 2006], nutrient cycling [Schilling and Lockaby, 2006], and biodiversity[Snodgrass et al., 2000; Gibbons, 2003]. Another reason for the selection of this watershed was the availabilityof long-term streamflow and groundwater data that could be used to validate the hydrologic model simula-tions. Physiography of the watershed is characterized by valleys and ridges oriented along the southwest-northeast direction. Watershed elevation ranges from 197 to 331 m (Figure 2a). Land cover in the watershedmainly consists of hay/pasture (37.6%), deciduous forest (32.9%), developed area (6.8%), and evergreen for-est (5.4%) (Figure 2b). The most common soil types in the watershed are loam in the riverbed and riparianregions and sandy clay loam in uplands (Figure 2c). The watershed falls in warm temperate climate withhumid and warm summer based on the Koppen-Geiger climate classification [Kottek et al., 2006]. Thirty yearaverage temperature in the watershed is 15.58C and annual precipitation ranges from 703 to 1473 mm.

2.2. Hydrologic Model2.2.1. Model DescriptionA physically based, fully distributed hydrologic model, Penn State Integrated Hydrologic Model (PIHM) [Quand Duffy, 2007; Kumar et al., 2009a; Kumar, 2009] was used to simulate coupled hydrologic states and proc-esses. PIHM has been previously applied at multiple scales and in diverse hydro-climatological settings[Kumar et al., 2013; Shi et al., 2013; Yu et al., 2014; Chen et al., 2015; Kumar and Duffy, 2015; Yu et al., 2015].The model uses a semidiscrete, finite-volume approach to discretize the model domain and solve the ordi-nary differential equations (ODEs) of multiple states such as surface water depth, soil moisture, groundwaterdepth, and river stage. Processes simulated in the model include evaporation, transpiration, infiltration,

Figure 2. (a) Elevation and USGS observation stations, (b) land cover type, and (c) soil type in the Second Creek watershed. Land cover inthe watershed include deciduous forest (DCF), developed low intensity (DVL), developed medium intensity (DVM), developed open space(DVO), and evergreen forest (EVF). Soil cover symbols are MUKEY from SURGGO data. CeB2, CeC2, PcB2, and PcC2 indicate sandy clayloam, ChA indicates loam, EnB and PaD indicate sandy loam, LdB2 and MeB2 indicate clay loam. Refer to Soil Survey Staff [1995] fordetailed information.



recharge, overland flow, subsurface flow, and streamflow. Evapotranspiration in the model is computedusing the Penman-Monteith method; overland flow is modeled using diffusion wave approximation ofdepth-averaged 2-D St. Venant equations; subsurface flow is based on Richards equation with movingboundary approximation; and stream channel routing is modeled with depth-averaged 1-D diffusive waveequation [Kumar, 2009]. Laterally, hillslopes and rivers are discretized using triangular grids and line ele-ments, respectively. Vertically, each triangle element consists of four layers: a surface layer, a 0.25 m thickunsaturated layer, an intermediate unsaturated layer extending downward from 0.25 m to the groundwatertable, and a groundwater layer. Soil moisture in the two unsaturated layers may vary from residual moistureto full saturation. As the average combined thickness of soil, saprolite, and the transition zone of regolithhas been estimated to be less than 20 m in the region [Daniel, 1989], a uniform depth of 20 m was consid-ered as the lower boundary of the subsurface layer. A spatially adaptive flexible domain discretizationscheme was used to generate the model grid. Given that this study concerns hydrologic dynamics in wet-lands, a hydrographic feature that accounts for less than 1% of the watershed area, a nested domain discre-tization [Kumar et al., 2009b] with a total of 4525 elements was used (Figure 4). Because of computationalconstraints, we focused our attention on the largest 10 wetlands with area ranging from 57,000 to167,000 m2. Elements smaller than 10,000 m2 were generated in and around these wetlands to improve therepresentational accuracy, while larger elements (smaller than 5,000,000 m2) were used away from the wet-lands to ensure computation efficiency. Number of discretization elements within the 10 wetlands rangedfrom 18 to 74, with an average size of 5710 m2. At each time step which was adaptively defined by a numer-ical ODE solver, ODEs of hydrologic states from all the elements were assembled and solvedsimultaneously.2.2.2. Model Parameterization, Calibration, and ValidationTo set up the model, we used the 30 m resolution elevation data from National Elevation Dataset (NED)[U.S. Geological Survey, 1999], USDA-NRCS Soil Survey Geographic (SSURGO) soil data [Soil Survey Staff,1995], and National Land Cover Dataset (NLCD) land cover data [Homer et al., 2015]. Meteorological forcingssuch as precipitation, air temperature, relative humidity, wind speed, and radiation were obtained fromNorth America Land Data Assimilation System Phase 2 (NLDAS-2) data [Xia et al., 2012], which has a spatialand temporal resolution of 1/88 and an hour, respectively. Ecological and hydrogeological parameters andmeteorological forcings relevant to the model simulation were automatically extracted from the raw datasets using an integrated model-GIS framework, PIHMgis [Bhatt et al., 2014].

As the goal of this study is to characterize the role of meteorological controls on interannual wet-period var-iations in wetlands, a long-term model simulation from 1981 to 2013 was performed. Calibration of modelparameters was performed using the observation data from 1993, which is a normal year with annual pre-cipitation of 1085 mm. The calibration year presented a range of meteorological conditions with large pre-cipitation events (e.g., 57 mm on 13 March 1993) and long dry periods with flow lower than the thirtiethpercentile for 112 days. The diverse hydrologic conditions during the calibration period allowed tuning ofmodel parameters such that the model could capture responses during both high and low flows. The firststep in the calibration process was initialization of the PIHM model with water table at the land surface. Themodel was then allowed to relax with no precipitation input until the streamflow recession rate matchedthe observed during the low-flow period in summer. The modeled streamflow magnitude was then com-pared with the observed value. The basis of this comparison is that streamflow during low-flow period islargely due to groundwater base flow, and hence a match between observed and modeled streamflowwould indicate reasonable estimation of the groundwater distribution in summer. During this process, thehydraulic conductivity of the subsurface was calibrated uniformly across the entire model domain[Refsgaard and Storm, 1996]. Then starting from the derived groundwater table initial condition, the modelwas forced with real meteorological inputs. After a 1 year warm-up period, the simulation results were com-pared against the observed streamflow and groundwater data at USGS guaging stations USGS 02120780and USGS 354057080362601, respectively (Figure 1a). Manual calibration of hydrogeological parameterssuch as soil hydraulic conductivity, macroporosity, and soil drainage parameters was performed in this step.Both the Nash-Sutcliffe efficiency (NSE) [Nash and Sutcliffe, 1970] and the log-transformed NSE (logNSE)were used to evaluate the accuracy of simulation results, as the two metrics emphasize on high and lowflows, respectively [W€ohling et al., 2013]. The modeled streamflow within the calibration period matchedthe observed data reasonably well, with NSE and logNSE of 0.84 and 0.87, respectively (Figure 3a). The mod-eled GWT also matched the observation well with NSE of 0.79.



The model simulation was validated using streamflow and GWT data from November 1989 to September2013. For the 24 year validation period, the daily and monthly streamflow NSE was 0.42 and 0.61, respec-tively. The daily and monthly logNSE for the same period was 0.72 and 0.69. For GWT, the daily and monthlyNSE was 0.59 and 0.62, respectively (Figure 3b). It should be noted that NSE for the daily streamflow timeseries was relatively low, in part because of the underprediction of streamflow in response to extremelylarge hurricane storms. This is partially attributable to NLDAS precipitation input that was used to drive thesimulation, which tends to be smaller than station observations [Luo et al., 2003], especially for large iso-lated events. If the largest 10 storm events with daily precipitation greater than 65 mm were discarded, thedaily NSE would rise up to 0.58.

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Figure 3. Comparison of modeled and observed streamflow and groundwater during (a) the calibration period (1993) and (b) thevalidation period (1989–2013).

Figure 4. Spatial distribution of model-detected wetlands and NWI wetlands.



To further evaluate the simulation results, wecompared the model identified wetlandswith the National Wetland Inventory (NWI)wetlands [U.S. Fish and Wildlife Service, 1993].Model-detected wetlands were locationswith simulated GWT being higher than20.3 m for at least two continuous weeks inthe growing season every other year. Thisdelineation procedure conforms withNational Research Council’s definition of wet-lands [Lewis, 1995]. The growing season usedfor wetland detection ranged from 26 Marchto 11 November in North Carolina [Tiner,1999]. The wetlands identified by the modelcorrespond well with the overall distributionof NWI wetlands (Figure 4). Fifty-eight per-cent of the wetland area detected by themodel overlapped with the NWI wetlands.

Possible reasons for the mismatch include (1) inaccurate representation of microtopography in the modeldue to coarse grid resolution; (2) inherent uncertainties in the NWI wetland boundaries [Tiner, 1999;Wardrop et al., 2007]; and (3) incompatibility in the definition of wetland used in NWI and this study. NWIwetlands were identified from high-altitude imagery based on vegetation, visible hydrology, and geography,whereas the model used groundwater dynamics to detect wetlands. Overall, the model was able to capturethe spatial distribution wetlands, which is a direct function of the spatiotemporal distribution of groundwaterin the watershed.

Validation of the long-term streamflow and GWT series at the gauging stations and the spatial distributionof wetlands established sufficient confidence in the PIHM simulation. The simulated GWT series in wetlandswere then used to study variations in wet-period characteristics in response to meteorological conditions.

2.3. Quantifying Wet-Period Characteristics and Their Dependence on Meteorological Controls2.3.1. Defining Wet-Period Characteristics and Meteorological ControlsIn this study, we quantified two wet-period characteristics: wet duration and start date (Figure 5). Wet dura-tion tracks the length of time for which GWT is higher than the critical threshold. This characteristic couldpotentially be used to estimate ecological functions of wetlands (see section 1). Together with wet duration,start date evaluates timing of wet-period in each year. These two characteristics can then be used to definethe prevailing environmental conditions during wet-periods, thus allowing more accurate quantification ofecological functions of wetlands [Christensen et al., 2003]. As GWT in the Second Creek watershed generallyincreases in autumn and winter and decreases in spring and summer, start date and wet duration wereextracted for an annual period starting from 1 September to 31 August of the next year. The annual period,referred hereafter as a ‘‘hydrologic year,’’ ensures that the GWT time series contains a single seasonal peakwith low GWT at the start and the end of year. The wetland GWT was quantified as the average across allthe elements within a wetland. Start dates and wet durations were then extracted for each hydrologic yearusing a 10 day moving average of daily GWT time series to smooth out transient daily fluctuations.

In line with our goals to evaluate the extent to which meteorological controls alone can be used to estimateand predict interannual wet-period variations in wetlands, here we consider Ppt and PET as the primarymeteorological variables for our analysis. The two variables were selected because of their widespread avail-ability and their influence on groundwater dynamics. Ppt and PET are expected to influence the wetlandGWT by modulating groundwater recharge and actual evapotranspiration (ET) from the wetland and byindirectly controlling the lateral flux exchange with the neighboring aquifer and streams. Ppt data are read-ily available for the entire continental US from national databases such as NCDC and NLDAS, while PET canbe obtained based on Penman-Monteith equation [Penman, 1948; Monteith, 1965] using relevant meteoro-logical data from NCDC and NLDAS data sets. As such, the methods presented in this paper can be used forother inland wetlands with available Ppt and PET data. Another notable advantage for choosing these twovariables is that their predictions are generally available from climate models [Hartmann et al., 2013], which

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Figure 5. Typical wetland groundwater table variation within a hydrologicyear.



makes it feasible to readily apply thepresented methods to understand thefuture impacts on wet-periodvariations.2.3.2. A Bayesian RegressionFramework for Estimation, Variableselection, and PredictionIn order to estimate and predict wet-period characteristics using the afore-mentioned meteorological controlsand to identify the relative seasonalcontributions for each meteorologicalvariable, a Bayesian linear regressionand variable selection method [Mitchelland Beauchamp, 1988; Hoff, 2009] wasimplemented. The Bayesian regressionmethod assumes a linear relationbetween a dependent variable yi and ap-dimensional independent variablex i5ðxi;1; xi;2; . . . ; xi;pÞ, with i51; . . . ; n.In this study, start date and wet dura-tion are used as a dependent variables.The independent variable is either Pptor PET or both. n 5 32 corresponds tothe length of simulation in years. Therelation between y5ðy1; y2; . . . ; ynÞT

and X5ðx1; x2; . . . ; xnÞT is expressedas

yi5z1b1xi;11z2b2xi;21 . . . 1zpbpxi;p1!i;

(1)

where i51; . . . ; n; !i is independent and identically distributed normal noise with a mean and variance of 0and r2, respectively; zj 2 f0; 1g; j51; . . . ; p indicates whether variable xi;j is included in the regression; andbj is the regression coefficient for variable xi;j ; T denotes the matrix transpose. In order to estimate y using X,the parameters of z5ðz1; z2; . . . ; zpÞT and b5ðb1; b2; . . . ; bpÞT are to be evaluated. Based on the Bayesianregression and variable selection framework shown in Figure 6, posterior distributions of the parameterswere derived by combining the prior distributions (equation (A3)) and the time series of X and y using equa-tion (A7) (see Appendix A for details). Based on the posterior distributions, 104 samples of each parameterwere drawn using Gibbs sampling, one of the most widely applied Markov Chain Monte Carlo (MCMC) algo-rithms [Bishop, 2006]. The running average and trace plot of each parameter were checked to ensure con-vergence. The first 103 samples of each parameter belonging to the burn-in period were discounted. Withthe remaining effective samples, the Bayesian regression coefficient of b5ðz1b1; z2b2; . . . ; zpbpÞT was com-puted as the average over the remaining samples, which is a simple case of Bayesian Model Averaging(BMA) [Hoeting et al., 1999]. The Bayesian estimated wet-period characteristics were then computed usingy5Xb.2.3.3. Estimating Wet-Period Characteristics Using Meteorological ControlsTwelve Bayesian regressions were generated for both start date and wet duration. The first three regres-sions used annual Ppt, PET, and both Ppt and PET as independent variables, respectively. The next threeregressions used the same independent variable configuration, but instead of the annual magnitudes, sea-sonal values of the variables in the four seasons, i.e., autumn (September–November), winter (December–February), spring (March–May), and summer (June–August), were used. Because of the inherent memory ofthe hydrologic system [Shook and Pomeroy, 2011; Nippgen et al., 2016], it is reasonable to expect that ante-cedent meteorological conditions may affect wet-period characteristics. To test this hypothesis, the follow-ing three regressions used seasonal magnitudes of Ppt and PET from the four seasons and an antecedent

Figure 6. Framework of Bayesian regression and variable selection. s denotes thegeneration of samples (s51; 2; . . . ; 104).



season from the previous hydrologic year. The antecedent season used here is the summer right before thestart of a hydrologic year. The final three regressions used two antecedent seasons, i.e., the previoussummer and spring in addition to the four seasons of a hydrologic year. In order to intercompare the effi-cacy of different variable configurations for estimating wet-period variations, we calculated the coefficientof determination (R2) for each Bayesian regression. The differences in R2 obtained using only Ppt, only PET,and both of them together would indicate the relative abilities of these two variables in explaining interan-nual wet-period variations. Similarly, comparison of R2 for regressions using either annual or seasonal mete-orological variables would highlight the role of seasonal forcings on wet-period variations. The comparisonbetween R2 obtained with zero, one, and two antecedent seasons would help evaluate the role of anteced-ent meteorological conditions on wet-period variations.2.3.4. Identifying the Controlling Seasons that Influence Wet-Period VariationsVariable selection, i.e., identification of the relative importance of each independent variable for capturingvariations in the dependent variable, was performed using the Bayesian framework. Since the frameworkselects the regression model that is likely to have high accuracy and small uncertainty, independent varia-bles that contain more effective information and introduce minimal uncertainty have a greater chance tobe included in the regression model. Under this mechanism, the probability for each variable to beincluded, which was approximated by the frequency of zj 5 1 (equation (1)) in the posterior effective sam-ples, represents how critical this variable is in explaining variations of the dependent variable, relative to allthe other independent variables. For example, in the Bayesian regressions that use seasonal Ppt, the proba-bility of zj 5 1 provides information on which seasonal Ppt is critical in capturing variations in start date orwet duration. High probability of zj 5 1 for a variable indicates that it is crucially needed to capture varia-tions in the dependent variable.2.3.5. Predicting Wet-Period Characteristics Using Meteorological ControlsThe Bayesian approach has been widely applied to make predictions as it generally improves the confi-dence in prediction by reducing uncertainties associated with parameter estimation [Thiemann et al., 2001;Jin et al., 2010]. After establishing the relation between meteorological conditions and wet-period character-istics using historical data, either from observations or a model, future response of wet-periods can be pre-dicted using projections of meteorological conditions. Here we evaluated the accuracy of the Bayesianestimator for predicting wet-period variations. Error estimates from the method represent the uncertaintyin prediction of wet-period characteristics. The 32 year time series was divided into two parts, a training anda testing set with 16 data points each. Using the training set, parameters of the Bayesian estimator wereobtained for each wetland separately. The estimator was then applied to quantify wet-period variations inthe testing set. To minimize bias in the performance of the testing set due to the choice of the training set,we rotated the training set for cross validation [Kohavi, 1995]. A full cross validation would involve C32

16 $63108 trials. To reduce the computational expense, we randomly generated 1000 mutually exclusivetraining and testing sets to quantify the errors.

3. Results and Discussions

3.1. Interannual Variations in Wet-Period CharacteristicsOver the 32 year study period (1981–2013), wet-periods generally started in autumn or early winter,reached groundwater peak in late winter or early spring, and ended in spring or early summer (Figure 7). Ofthe 320 simulation years (532 years 3 10 wetlands), 75% had wet-periods spanning from 3 to 8 monthsand 56% had wet-periods spanning from 4 to 7 months in a year. Median of start date and wet durationwas 13 November and 164 days, respectively. The simulated temporal distribution and duration ranges aremostly consistent with those observed in the forested wetlands in South Carolina and Louisiana [Megonigalet al., 1997], which lie in the same climatological classification region as North Carolina [Kottek et al., 2006].The results also show that large temporal variations exist in wet-periods (Figure 7). Start date varied by sev-eral months or even seasons. For instance in wetland 1 (Figure 7), start date varied from 5 September (in2003) to 17 March (in 2001), with an average variation range of 194 days and a standard deviation of 45days. Also, the wet duration in wetland 1 ranged from 47 to 275 days with a standard deviation of 55 days.In wetland 7, wet duration was as long as 196 days in 1992, but was zero in 2001 as the GWT was neverhigher than 20.3 m during the year. Since meteorological variables are the primary dynamic forcings that



are expected to drive interannual var-iations in wet-period variations[Changnon et al., 1988; Reich et al.,2002; von Asmuth and Knotters, 2004],next we quantify their influence onwet-period characteristics.

3.2. Estimation of Wet-PeriodCharacteristics Using MeteorologicalControlsAnnual precipitation amount isexpected to be inversely related withstart date and positively related withwet-period duration. This is becausehigher annual precipitation tends toenhance the groundwater recharge,which should result in an earlier startand longer duration of wet-periods. Incontrast, annual PET is expected to bepositively related with start date and

inversely related with wet duration, as higher atmospheric demand for moisture should enhance waterlosses resulting in a delayed start date and a shorter wet duration. However, Bayesian regression resultsusing annual precipitation showed that the annual magnitudes only explained a small part of variation instart date and wet duration, with average R2 of 0.172 and 0.437, respectively, for the 10 wetlands (Table 1,column 1). By combining annual PET with precipitation in the regression, the average R2 increased margin-ally to 0.193 and 0.478 (Table 1, column 3). Remarkably, the average R2 improved significantly from 0.193 to

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Spr.

Sum.Start Peak End

Figure 7. Box plot of start date, peak date and end date of wet-periods for the 10wetlands in Second Creek watershed. The lower and upper edges of the boxesrepresent the 25th and 75th percentiles, respectively. The whiskers around theboxes extend to the most extreme data points except for outliers.

Table 1. R2 for the Twelve Bayesian Regressions Used to Estimate Start Date and Wet-Period Duration in the Wetlands of Second CreekWatersheda

Start Date

AN SN SN1AT1 SN1AT2

WetID Ppt PET Both Ppt PET Both Ppt PET Both Ppt PET Both(0) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12)

1 0.097 0.049 0.100 0.517 0.335 0.550 0.710 0.355 0.711 0.724 0.353 0.7242 0.087 0.099 0.128 0.605 0.500 0.708 0.622 0.498 0.729 0.699 0.498 0.7563 0.265 0.281 0.353 0.593 0.538 0.693 0.655 0.544 0.708 0.685 0.551 0.7124 0.218 0.130 0.215 0.661 0.480 0.736 0.706 0.481 0.764 0.723 0.483 0.7715 0.214 0.075 0.200 0.548 0.340 0.624 0.674 0.350 0.686 0.692 0.350 0.6966 0.423 0.114 0.422 0.609 0.344 0.648 0.662 0.361 0.700 0.683 0.358 0.7037 0.144 0.098 0.160 0.461 0.329 0.527 0.623 0.334 0.618 0.655 0.342 0.6338 0.140 0.076 0.151 0.517 0.366 0.589 0.536 0.382 0.629 0.560 0.391 0.6419 0.022 0.059 0.071 0.226 0.309 0.363 0.375 0.312 0.444 0.442 0.322 0.50010 0.109 0.081 0.128 0.599 0.444 0.675 0.714 0.444 0.720 0.721 0.444 0.729Avg. 0.172 0.106 0.193 0.534 0.399 0.611 0.632 0.409 0.671 0.658 0.409 0.687

Duration1 0.455 0.246 0.457 0.590 0.378 0.609 0.732 0.432 0.749 0.734 0.437 0.7512 0.367 0.284 0.411 0.720 0.488 0.779 0.752 0.498 0.784 0.760 0.498 0.7893 0.473 0.513 0.611 0.733 0.682 0.833 0.771 0.688 0.841 0.773 0.701 0.8444 0.462 0.381 0.507 0.741 0.595 0.806 0.773 0.605 0.815 0.773 0.606 0.8175 0.440 0.295 0.458 0.677 0.559 0.743 0.715 0.561 0.788 0.715 0.563 0.7896 0.397 0.143 0.397 0.518 0.418 0.543 0.601 0.429 0.621 0.600 0.430 0.6217 0.378 0.337 0.412 0.605 0.563 0.673 0.670 0.564 0.752 0.672 0.573 0.7588 0.472 0.363 0.532 0.819 0.615 0.858 0.826 0.613 0.874 0.828 0.623 0.8759 0.523 0.345 0.564 0.351 0.319 0.485 0.402 0.353 0.525 0.414 0.354 0.53210 0.407 0.313 0.432 0.626 0.523 0.740 0.750 0.545 0.773 0.752 0.546 0.775Avg. 0.437 0.322 0.478 0.638 0.514 0.707 0.699 0.529 0.752 0.702 0.533 0.755

aThe regressions used either precipitation (Ppt) or potential evapotranspiration (PET) or both Ppt and PET (Both) as independent vari-ables. Annual magnitudes (AN) of the independent variables or their seasonal magnitudes in four seasons (SN) with an option to useone (AT1) or two (AT2) antecedent seasons were used for regression. Four cases with no wet-period were excluded from calculations.



0.611 and 0.478 to 0.707 for start date and wet duration, respectively (Table 1, columns 3 and 6), wheninstead of the annual variables, seasonal Ppt and PET were used. The significant improvements in R2 indi-rectly indicate that the meteorological conditions in each season do not exert uniform impact on interan-nual variations of wet-periods.

Combining seasonal PET with seasonal Ppt improved the estimation accuracies further, with the average R2

increasing from 0.534 to 0.611 and 0.638 to 0.707 for start date and wet duration, respectively (Table 1, col-umns 4 and 6). To identify the conditions under which improvement in the estimation accuracy was large,wetland characteristics simulated by the PIHM model and those estimated using the Bayesian regressionswith only seasonal Ppt and both seasonal Ppt and PET were compared (Figure 8). The results indicate thatPET mainly improved the estimation for cases with late start date (later than the 150th day) or short wet-period duration (shorter than 4 months), which are general characteristics of dry years (years with small pre-cipitation) (Figures 8b and 8d). For example, wet duration for wetland 3 in 2010, a dry year with annual pre-cipitation of 874 mm, was 44 days based on the PIHM simulated GWT. If only seasonal precipitation wasused in the regression, the duration was overestimated to be 83 days. After incorporating both seasonalPET and Ppt in the regression, the estimated duration reduced to 58 days (Figure 8c). This improvementcould be attributed to the large PET of 1635 mm in 2010 (much higher than the long-term average of1405 mm) that shortened the wet duration. In fact, more than 70% of all the cases showing late start dateor short wet-period duration were characterized by a simultaneous occurrence of small Ppt (<40th percen-tile of annual Ppt) and large PET (>60th percentile of annual PET). These results indicate that by consideringseasonal PET in addition to seasonal Ppt in the Bayesian regression, wet-periods with extremely late startdates and short durations can be captured more accurately. To sum up, seasonal precipitation was able to

Figure 8. Performance comparison for estimating the (a) start date and (c) duration using merely seasonal Ppt, and both seasonal Ppt and seasonal PET (Ppt and PET). The improvementsby PET for the (b) start date and (d) duration were calculated as jy Ppt2yj2jy Ppt&PET 2yj, where the y Ppt ; y Ppt&PET , and y are the estimations by Ppt, Ppt, and PET using Bayesian methodand the base values simulated by the hydrologic model, respectively. The average improvements over an interval of 30 days were plotted using dark horizontal lines.



capture most of the variations in start date and wet duration on its own. Further improvement in estimationaccuracy was registered, especially for years with late start or short wet-period duration, by incorporatingseasonal PET in the regressions.

The estimation accuracy improved furthermore when in addition to the four seasons of a hydrologic year,one antecedent season, i.e., the previous summer, was also included in the regression (SN 1 AT1). By con-sidering the antecedent season, average R2 increased from 0.611 to 0.671 and 0.707 to 0.752 for start dateand wet duration, respectively (Table 1, columns 6 and 9). When one more antecedent season, i.e., the pre-vious spring, was also considered in the regression (SN 1 AT2), the R2 only increased marginally by 2.4%(from 0.671 to 0.687) and 0.4% (from 0.752 to 0.755) for start date and wet duration, respectively (Table 1,columns 9 and 12). These results indicate that although wet-periods were influenced by antecedent meteor-ological conditions, the influence was negligible for meteorological conditions beyond one antecedentseason.

Notably, the estimation accuracies of wet duration in wetland 6 and 9 were relatively low (Table 1, column9). This was partly because isolated precipitation events could raise the GWT height above the 20.3 mthreshold in these two wetlands, thus masking out the effects of seasonal forcings. In wetland 6, bank over-flow from a nearby stream, which inundated the wetland after large autumn and winter storms, generallyraised the GWT above the threshold (see Figure S1 in Supporting Information). In wetland 9, the GWT waswell near the 20.3 m threshold at the beginning of autumn (Figure S1). As such, isolated precipitationevents in autumn were able to lift the GWT above the threshold. Also, a few weeks without precipitationnear the end of the hydrologic year could let the GWT drop down. These results indicate that the seasonalmeteorological conditions may not capture wet-period variations when (1) response of GWT to isolated pre-cipitation events is larger than or comparable to its seasonal variation or (2) GWT is close to the criticalthreshold throughout the year.

3.3. Relative Role of Seasons in Controlling Wet-Period CharacteristicsAs indicated in section 3.2, Ppt and PET do not exert a uniform influence throughout a hydrologic year.Using the SN 1 AT1 regression configuration, next we identify the controlling seasons for Ppt and PET inregard to their role in estimation of wet-period characteristics.3.3.1. Identifying Seasons that Control Start DatesAmong the five seasons considered for regression, start date was found to be dominantly controlled byautumn precipitation, followed by precipitation in the previous summer. Other seasons had relatively lim-ited influence (Figure 9a). As wet-periods generally started in late autumn or early winter for most wetlands(Figure 7), the seasons that occur before the start date, i.e., the previous summer and autumn, were natu-rally detected as controlling seasons. For wetlands wherein wet-periods started in mid or late winter, suchas wetland 3, 5, 6, 7, and 8 (Figure 7), start date was also influenced by winter precipitation. Notably, eventhough wet-periods usually started in autumn, which means that only part of autumn precipitation (beforethe start date) could have affected the variation in start date, autumn still had the strongest influence inmost wetlands (Figure 9b). Wetland 9 was an exception in the sense that the previous summer had thestrongest influence in this case, as wet-periods usually started right at the beginning of autumn (Figure 7).Relative dominance of autumn precipitation with respect to the previous summer can be explained by firstconceptualizing start date as a function of initial GWT (iGWT) at the beginning of each hydrologic year (orthe end of the previous summer), and the GWT increasing rate (rGWT) from the beginning of autumn to thestart date (Figure 5). Next, influence of iGWT and rGWT on variations in start date was evaluated. For this,standard deviation of start date was calculated by (1) assuming that iGWT for each year was identical andequal to the long-term average iGWT, while rGWT varied across different years; (2) assuming rGWT for eachyear was identical but iGWT varied across different years. Average standard deviation of start date for thetwo cases were 83 and 28 days, respectively. Larger standard deviation in the first case, i.e., with constantiGWT and variable rGWT, indicates that rGWT played a bigger role in influencing start date. A smaller contri-bution of iGWT, which is directly correlated with summer Ppt (correlation coefficient, r 5 0.79), was a resultof groundwater relaxation in summer which led to a diminished variance in GWT in late summer. SincerGWT had a much stronger influence on start date, and as rGWT was largely determined by autumn Ppt(r 5 0.74), autumn was identified as the most dominant season.



Following a similar line of inquiry, relative roles of seasonal PET were evaluated. Although both autumn andthe previous summer PET were expected to affect start date, only autumn was detected to have a signifi-cant influence (Figures 9c and 9d). This is because rGWT, which is the primary control on start date, isaffected by autumn PET. The influence of summer PET was relatively small because (1) its impact on rGWTwas negligible and (2) the correlation between actual ET and PET in summer was smaller (r 5 0.61) than thatbetween ET and PET in autumn (r 5 0.82).3.3.2. Identifying Seasons that Control Wet DurationsIn regard to the seasonal influence of precipitation on wet duration, autumn precipitation was the mostdominant. Notably, precipitation in the previous summer, winter, and autumn also had moderate influenceon variations in wet duration (Figure 10a). Since wet-periods generally spanned from autumn to spring (Fig-ure 7), precipitation in the previous summer and autumn affected wet duration via the start date while pre-cipitation in winter and spring affected wet duration via the end date. For start date, as discussed in section3.3.1, precipitation in autumn contributed more than precipitation in the previous summer. For the enddate, in wetlands with long average wet durations (155–270 days), such as wetland 1, 2, 4, 6, and 10 (Figure7), precipitation in spring contributed more than that in winter (Figure 10b). In these wetlands, the GWTwas generally near the ground surface during winter. Precipitation during winter promoted discharge fromwetland into the river, which prevented the GWT from rising as much as it would happen when the GWTwas deep to begin with (Figure S1). Therefore, wet duration was less sensitive to winter precipitation forthese wetlands. In contrast, GWT variation in spring, which was much larger (20.43 m) than in winter(10.13 m), was influenced by the spring precipitation amount. As a result, spring precipitation exerted rela-tively larger influence on the end date and hence the wet duration. However for wetland 9, which alsoshowed long wet durations (Figure 7), wet duration variations were not captured well using seasonal

Figure 9. Relative seasonal influence on the interannual variations of start date by (a) Ppt and (c) PET, for the 10 wetlands. Individual seasonal contribution for each wetland by (b) Pptand (d) PET is presented in the colored table. Darker blue cells indicate larger contributions and vice versa. Smaller contributions in gray in Figures 9b and 9d indicate noisy anticorrela-tions of respective seasons on the dependent variables, and have been left out for calculating the average contributions in Figures 9a and 9c.



meteorological variables due to the strong event-scale effects. Hence, a clear seasonal influence of Ppt wasnot detected for this wetland. For wetlands 3, 5, 7, and 8, wherein average of wet duration was short (<130days) (Figure 7), winter precipitation contributed more than spring precipitation (Figure 10b). In these wet-lands, due to the late start of wet-periods, the net vertical recharge and lateral incoming fluxes were notlarge enough to saturate the wetland. As a result, the winter precipitation affected the GWT change moreeffectively; that is, precipitation before the peak date influenced the maximum GWT and that after the peakdate influenced the decreasing rate. Since wet-periods in these wetlands generally ended in early to mid-spring, the impacts of spring precipitation was muted. To sum up, wet duration was mostly controlled byprecipitation in autumn via the start date, and precipitation in winter or spring (depending on the length ofwet duration) via the end date.

PET in autumn, winter, and spring influenced wet duration more uniformly (Figures 10c and 10d). Giventhat the previous summer PET contributed little to start date (as discussed in section 3.3.1), its influence onwet duration was also muted. Winter and spring PET affected wet duration via the end date. Larger PET inwinter led to smaller maximum GWT and faster GWT recession, thus shortening the wet duration. Thespring PET also contributed to wet duration via the rate of GWT recession. As start date showed a larger var-iation range than end date (Figure 7), and as autumn was the only dominant season for start date, autumnPET had a slightly larger contribution than winter and spring.

3.4. Predicting Wet-Period CharacteristicsThe Bayesian estimator was able to predict start date with errors smaller than 2 weeks, 3 weeks, and 1month at confidence levels of 32.8, 73.1, and 95.1%, respectively (Figure 11). Corresponding errors for wet

Figure 10. Relative seasonal influence on the interannual variations of wet duration by (a) Ppt and (c) PET, for the 10 wetlands. Individual seasonal contribution for each wetland by (b)Ppt and (d) PET is presented in the colored table. Darker blue cells indicate larger contributions and vice versa. Smaller contributions in gray in Figures 10b and 10d indicate noisy anti-correlations of respective seasons on the dependent variables, and have been left out for calculating the average contributions in Figures 10a and 10c.



duration were predicted at confidence levelsof 14.3, 58.4, and 93.6%, respectively. Eventhough the Bayesian estimator was trainedusing the GWT and meteorological condi-tions of only 16 years, both start date andwet duration could be predicted with errorssmaller than 1 month at a 90% confidencelevel. Lower prediction errors are expectedfor longer available time series. Consideringthat start date and wet duration varied byseveral months or even seasons among dif-ferent years, these results indicate that theBayesian estimator can serve as an effectivetool for predicting start dates and wet dura-tions. Notably, start date and wet durationcan be estimated with even higher R2 usingthe OLS method, as its goal is to minimizethe squared error. For example, R2 for OLS

regression of start date and wet duration is 0.699 and 0.759, respectively, which is slightly higher than thatof 0.671 and 0.752 obtained using the Bayesian estimator, respectively (Table 1, column 9). However, theBayesian estimator is preferable for the purpose of prediction, as it is able to predict with much less errorthan the OLS estimator (Figure 11). For example, at a 90% confidence level, the OLS estimator predictedstart date with an error up to 67 days, while the corresponding error based on the Bayesian estimator wasless than 28 days.

4. Conclusions and Implications for Future Research

This study evaluated interannual variations in wet-period characteristics of 10 inland forested wetlands in asoutheastern US watershed, and quantified the extent to which these variations can be explained based onannual or seasonal meteorological conditions, specifically precipitation and potential evapotranspiration.The main conclusions and limitations of this study, and its implications for future research are as follows:

1. Start date and duration of wet-periods in the forested wetlands of the southeastern US exhibit significantinterannual variations. Among the 10 studied wetlands, the start date could be as early as September oras late as March, and the wet duration could vary by more than 6 months. As multiple ecological func-tions of wetlands such as greenhouse gas emissions [Moore and Knowles, 1989; Moore and Dalva, 1993;MacDonald et al., 1998; Strack et al., 2004; Jungkunst and Fiedler, 2007; Turetsky et al., 2008] and nitrogencycling [Hefting et al., 2004] are influenced by wet-periods (see section 1 for literature review), it isexpected that the ecological functions of wetlands may also vary significantly through the years. Notably,although wet-periods strongly influence wetland functions, more accurate estimation of interannual var-iations in the ecological functions should account for the influence of other physical controls such aswetland ecology and substrate characteristics [Ramirez et al., 2015].

2. The annual meteorological conditions could only capture 19.3 and 47.8% of the variations in start dateand wet duration, respectively, indicating that a longer or shorter wet-period in a year cannot beexplained simply based on if the year is wet or dry. Limited ability of annual variables to explain interan-nual variations in wet-period characteristics can be attributed to nonuniform influence of seasonal mete-orological conditions on wet-period variations. In the studied wetlands, meteorological conditions inautumn were identified to be the most dominant in influencing wet-period variations. This is expectedto be true for other forested wetlands in the southeastern US, as hydro-climatology in the region is char-acterized by autumn and winter that act as recharge periods [Anderson and Emanuel, 2008]. The relativedominance of autumn indicates that between 2 years with identical annual precipitation, the one with awetter autumn is more likely to experience an earlier start date and longer duration of wet-period,potentially causing larger methane emissions and denitrification rates. The results also indicate that forfuture predictions of wet-period characteristics and associated ecological functions, robust projections ofmeteorological conditions at least in the dominant seasons are paramount.

ERR of start date (day)10 20 30 40

CD

F

0

0.2

0.4

0.6

0.8

1

32.8%

14d

73.1%

21d

95.1%

30d

ERR of duration (day)10 20 30 40

14.3%14d

58.4%

21d

93.6%

30d

Bayesian OLS

Figure 11. Cumulative density functions (CDF) of the prediction error(ERR 5 jy Ppt&PET 2yj) for start date and wet duration using Bayesian andOLS regression methods.



3. Sixty to ninety percent of the variations in wet-period characteristics could be captured by the Bayes-ian regression using seasonal Ppt and PET as independent variables. As the two meteorological varia-bles are readily available within the continental US, the methods presented in this paper can easily beused for other inland wetlands. The efficacy of the framework for inland forested wetlands suggestthat the method can be used for wetlands wherein temporal GWT dynamics are primarily driven byPpt and PET in the regional watershed. However, the framework may not be as accurate for wetlandswhere isolated precipitation events could raise the GWT above the wet-period threshold (see detailssection 3.3.1). These wetlands are generally expected to have GWT height near the wet-period thresh-old. The applicability of this framework is also likely to be limited for wetlands where GWT dynamicsmay be affected by tidal fluxes (e.g., coastal wetlands) or irrigation (e.g., agricultural wetlands). Futurework should include testing the robustness and applicability of the framework in diverse climatic andhydrogeological settings.

4. Estimation accuracy of wet-periods was higher when in addition to the four seasons within a hydrologicyear, meteorological conditions in an antecedent season were also considered. However, an additionalantecedent season made negligible improvement to the estimation accuracy. This highlights that inher-ent hydrologic memory of the wetlands should be appropriately accounted for while estimating and pre-dicting interannual wet-period variations. Although hydrologic memory of groundwater systems mayvary with climatological forcings and watershed properties [Nippgen et al., 2016], the Bayesian frameworkpresented here is flexible enough to incorporate varied lengths of hydrologic memory, which can beidentified using the method discussed in section 2.3.3.

5. In the studied wetlands, errors for predicting start date and wet duration were less than 1 month at a90% confidence level, indicating that the Bayesian regression and variable selection framework providesan effective approach to predict interannual wet-period variations. By pairing it with short-term observa-tion experiments, the presented framework could potentially be applied to evaluate long-term variationsin wetland ecological functions. For example, the framework may be first used to predict wet-period var-iations using Ppt and PET projections from climate models. Concurrently, a quantitative relation betweenwet-period and ecological functions, such as methane emissions, may be established via short-termobservation experiments [e.g., Nyk€anen et al., 1998; Altor and Mitsch, 2006]. The derived relation can thenbe used with the predicted wet-periods to evaluate the impacts of climate change on methane emis-sions from wetlands. However, as the relation between GWT and ecological functions are often site-specific and may vary a lot among wetlands [Walter and Heimann, 2000; Turner et al., 2016], it is impor-tant to first verify the applicability of GWT vs. ecological function relation at a site before the frameworkis applied for future predictions. In order to use the results for decision making, appropriate uncertaintycharacterization should also be performed.

6. In this study, wet-periods were defined based on a GWT threshold of 20.3 m. However, depending onthe ecological function of interest and the vegetation, substrate, and meteorological properties, the criti-cal GWT threshold in some wetlands may differ from 20.3 m. For example, methane emission rates froma Ohio riparian wetland [Altor and Mitsch, 2006] and a Michigan peatland [Shannon and White, 1994]were observed to be much higher when GWT was higher than 20.2 and 20.15 m, respectively. It is sug-gested that appropriate thresholds should be chosen based on the site-specific relation between GWTand the ecological function of interest. Notably, the Bayesian framework used in this study is flexibleenough to incorporate different thresholds.

7. While the presented Bayesian framework should ideally be trained using long-term observed ground-water data, in the absence of observed data, a physically based model may be used to generate long-term groundwater time series in wetlands. However, accuracy of the Bayesian approach in this case isbound to be dependent on the model’s ability to simulate GWT in wetlands. In this study, even thoughthe PIHM results were extensively validated against multiple observations, uncertainty in the simulatedwet-period characteristics cannot be overlooked. Further confidence in the modeled results and the anal-yses could be established by validating against additional observations.

In spite of the aforementioned limitations, the study highlights an undeniable influence of seasonalityand hydrologic memory on wet-period variations of inland forested wetlands. The presented frameworkprovides a simple, yet effective, approach for estimating and predicting wet-period variations in inlandwetlands. The approach can also be used to estimate variations in associated ecological functions inwetlands.



Appendix A: Derivation of the Posterior Distributions

Let X be the n 3 p matrix of ðx1; x2; . . . ; xnÞT, where x j5ðxj;1; xj;2; . . . ; xj;pÞ; ðj51; . . . ; n). Letb5ðz1b1; . . . ; zpbpÞT, then based on equation (1)

fyjX; b; r2g % multivariate normalðXb; r2IÞ: (A1)

Hence, the likelihood of the time series y is

pðyjX; b; r2Þ / exp 21

2r2 yTy22bXTy1bTXTXb! "# $

: (A2)

Considering that our goal is to estimate and predict y using X, one needs to estimate the parametersb and r2.

The prior distributions for z5ðz1; . . . ; zpÞT; b5ðb1; . . . ; bzÞT and r2 are obtained as follows. For each zj, a

noninformative Bernoulli prior of Prðzj50Þ5Prðzj51Þ51=2 is used. For b and r2, Zellner’s g-prior [Zellner,1986] and inverse-gamma prior is applied, respectively (equation (A3)).

zj % Bernoullið1=2Þ;

bz % Multivariate normal ð0; gr2ðX zTX zÞ21Þ; (A3)

r2 % Inverse2gammaðm0=2; m0r20=2Þ;

where for any given z with pz being the nonzero entries, bz is a pz31 vector consisting of all nonzero entriesin z; and Xz is a n3pz matrix corresponding to nonzero entries of z. The Zellner’s g-prior is a widely usedprior distribution for regression parameters, which provides a closed-form representation of marginal likeli-hoods and hence is computationally efficient [Liang et al., 2008]. Specifically, unit information prior [Kassand Wasserman, 1995], a type of weakly informative prior, is provided for bz and r2 by choosing priorparameters of g5n; m051;r2

05r2ols, where r2

ols5ðy2XbÞTðy2XbÞ=ðn2pÞ is the ordinary least squares(OLS) estimate of r2. The multivariate normal prior for bz and the inverse-gamma prior for r2 are semi-conjugate for the multivariate normal model (equation (A1)), which enables the posteriors to be derivedanalytically.

Next, the posterior distributions for z;b and r2 are derived. According to the Bayes theory, the posterior ofz can be computed using:

pðzjy;XÞ5 pðzÞpðyjX; zÞR~z pð~zÞpðyjX; ~zÞ

; (A4)

where ~z denotes all the possible values of z, i.e., 0 and 1. For each zj, in order to calculate the posterior prob-ability for zj 5 1, let za5ðz1; . . . ; zj51; . . . ; zpÞT and zb5ðz1; . . . ; zj50; . . . ; zpÞT. Then based on equation (A4),the posterior odds of za and zb are calculated using:

oj5pðzajy;XÞpðzbjy;XÞ

5pðzaÞpðzbÞ

pðyjX; zaÞpðyjX; zbÞ

; (A5)

where the marginal likelihood of z is

pðyjX; zÞ5ð ð

pðy; b; r2jX; zÞdbdr2

5ð ð

pðyjb; XÞpðbjX; z; r2Þpðr2Þdbdr2: (A6)

Equation (A6) can be integrated analytically by plugging in the priors (equation (A3)) and the likelihood(equation (A2)) (see Hoff [2009] for details). With the posterior odds computed (equation (A5)), each zj canbe evaluated using a Bernoulli distribution (equation (A7)). Then for a given z, by combining the likelihood(equation (A2)) and the semiconjugate priors (equation (A3)), the posteriors of bz and r2 can be obtained asfollows:



Prðzj51jy; X; z%jÞ5Bernoulliðoj=ðoj11ÞÞ;

pðbzjy;X z; r2Þ / pðyjXz; bz; r2Þ3pðbzÞ / multivariate normalðln;RnÞ; (A7)

pðr2jy;XzÞ / pðyjX z; r2Þ3pðr2Þ / inverse2gammaðmn;CnÞ;

where z%j represents all the entries in z except for zj; ln5g=ðg11ÞðXzTXzÞ21Xz

Ty;Rn5g=ðg11Þr2ðXz

TXzÞ21; mn5ðm01nÞ=2; Cn5ðm0r20z1SSRgzÞ=2; r2

0z5ðy2XzbzÞTðy2XzbzÞ=ðn2pzÞ;

SSRgz5yTðI2g=ðg11ÞXzðXzTXzÞ21Xz

TÞy.

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