Assimilation of near-surface cosmic-ray neutrons improves summertime soil moisture profile estimates at three distinct biomes in the USA

Assimilation of near-surface cosmic-ray neutrons improves summertime soil moisture profile estimates at three distinct biomes in the USA R. Rosolem, T. Hoar, A. Arellano, J. L. Anderson, W. J. Shuttleworth, X. Zeng, and T. E. Franz Queens School of Engineering, University of Bristol, Bristol, UK NCAR Data Assimilation Research Section, Boulder, USA Department of Atmospheric Sciences, University of Arizona, Tucson, USA Department of Hydrology and Water Resources, University of Arizona, Tucson, USA School of Natural Resources, University of Nebraska-Lincoln, Lincoln, USA


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In order to produce a continuous set of hourly meteorological forcing data for each site 28 for the period of interest (May through September 2012), the following data gap filling 29 rules were applied following (Rosolem et al., 2010): 30 i.If the gap was less than 3 hours, it was filled by linear interpolation.
ii.If the gap was greater than 3 hours, the missing hours were replaced by values for the 1 same hours averaged over the previous and subsequent 15 days.

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iii.If any additional gap filling was needed, the missing data were replaced by the 3 average value for the specific hour calculated in the monthly mean diurnal cycle.(NCEP) for coupled weather and climate modeling (Ek, 2003) was adopted in this study.

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This LSM is also used in the NASA Land Information System (LIS) (Kumar et al., 2008), and in the Global (Rodell et al., 2004) and North American (Mitchell, 2004) Land Data 10 Assimilation Systems (GLDAS and NLDAS, respectively).

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The model contains four soil layers that extend two meters below the surface; 12 specifically, a 10-cm thick surface layer, a 30-cm thick root zone layer, a 60-cm thick soil moisture applications (Franz et al., 2012b;2013b;Rosolem et al., 2013).Here, the 1 COSMIC is used to convert soil moisture profiles derived from the Noah into an 2 equivalent neutron intensity as seen by a cosmic-ray sensor.The code has been 3 developed as part of the COSMOS network and is available at 4 http://cosmos.hwr.arizona.edu/Software/cosmic.html.order to estimate the state of a physical system while recognizing both have some 9 degree of uncertainty.Given the complexity of geophysical models in general, ensemble 10 data assimilation techniques were originally developed to decrease the computational 11 cost of the nonlinear filtering problem patterned after the Kalman filter (Kalman, 1960; 12 Kalman and Bucy, 1961) by using a sample of model-state vectors to compute their 13 statistical moments (i.e., mean and covariance) (Evensen, 1994;2003

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The ensemble data assimilation method used in this study is an approximation to a

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where x is the model state variable, Y is the set of all observations that have already

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been assimilated which does not include the new observation, y, available at the current 30 time, and η refers to a normalization factor.The ensemble assimilation procedure is

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(1) Each ensemble member is advanced from the time of the most recently used 1 observation to a time sufficiently close to the time of the next available observation using 2 the Noah.

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(2) A prior ensemble estimate of y is created by applying the forward operator h (in this 4 case, COSMIC) to each sample of the prior state.

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(3) An updated ensemble estimate of y conditioned on the new observation is computed 6 from the prior ensemble estimate of y and the observed value, y o , using Eq. ( 1).In this  per integration time (i.e., hourly), the assumption of observation uncertainty to be Normal( !,  !! ) in Eq. ( 1) is computed resulting in a Gaussian updated distribution for y,

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respectively.In the EAKF, the prior ensemble distribution of y is then shifted and linearly 20 contracted to create an updated ensemble with sample statistics as in Eqs. ( 2) and (3).

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Observation increments are computed as

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where the subscript i refers to ensemble member.

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(4) Increments to the prior ensemble of each state-vector element (x j,i , where j refers to

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an element of the state vector, while i refers to an ensemble member) are computed by

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independently using the prior joint sample statistics, so that: 1 The Noah, the COSMIC operator and COSMOS observations have all been 2012).This is because we want to preserve the site-specific count statistics to better 20 describe measurement uncertainty (lower count rates, on average, will tend to be more

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uncertain compared to locations where count rates are relatively high).Moreover, there

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are no systematic biases between observed and simulated neutron counts (not shown),

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and data assimilation is performed with zero-mean random errors only (Dee, 2005).

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Observing System Simulation Experiments (OSSE) such as those proposed in this study   the no Data Assimilation case (i.e., 'no DA') (Figure 4).The ensemble mean of the prior 5 distribution is used for all ensemble simulations throughout this study.As discussed in 6 Section 1, the higher the neutron counts at a specific location, the lower the integrated soil moisture is expected to be.Rainfall events are therefore associated with sharp 8 decreases in the neutron counts following by a relatively slower dry-down period. 9 Noticeably, the Kendall site (Figure 4a) is characterized by an initial long period with very 10 low or no rain (pre-monsoon) until early-July, followed by more frequent rainfall events    3).Overall, the 'DA 1-hour' case approaches more

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rapidly to the true neutron counts and also exhibits a tendency for relatively smaller

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differences when compared to the 'DA 2-day' case.Notably, at the onset of the monsoon

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at Kendall (i.e., early-July), the low frequency assimilation case does not reproduce the 24 high-frequency dynamics as well as the 'DA 1-hour' case (Figure 4a).At the Nebraska

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and Park Falls sites (Figures 4b and 4c), there is not much improvement in Noah-

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derived neutron counts from the 'DA 2-day' relative to the 'no DA' in periods where little

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or no rainfall occurs.

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The use of synthetic observations ensures that the neutron signal from the measurement 29 comes from direct contribution of soil moisture dynamics solely, and that any model 30 structural deficiency does not impact the results.Hence, a potential limitation of an

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OSSE is that the results can be very optimistic in comparison to a data assimilation 32 experiment using real observations.For instance, when comparing against real

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As expected, the time at which rainfall occurs appears to control the characteristics of 25 both statistical quantities.We therefore identified two patterns that emerged in Figure 5.

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The first pattern is associated with a rapid increase in both RMSE and spread during 27 large rainfall events (rapid reduction in neutron counts as shown in Figure 4).These are 28 more clearly observed for the 'DA 2-day' cases (middle-column) at Kendall (mid-May,

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early-July, mid-August, and early-September) and at Nebraska (mid-July, late-August,

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and mid-September).These peaks are substantially reduced when observations of 31 neutron counts are assimilated at higher frequency (i.e., 'DA 1-hour' as shown in the 13 right column).No large rainfall event was identified at the Park Falls site (Figure 4). 1 Consequently, this pattern was not observed in Figure 5.

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The second pattern relates to the overall timing of the summer rainfall.At the Kendall 3 site, once the monsoon period begins (early-July), the assimilation of observations 4 successfully constrains the model which produces consistent equivalent neutron counts

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(Figures 5b and 5c).In other words, rainfall pulses provide "new information" to the 6 assimilation system.For the two other sites (Nebraska and Park Falls), an active rainfall 7 period lasts until early-July and is then followed by a period of low or no rainfall 8 (arguably, no substantial "information" to the assimilation system).In this case, we 16 Finally, the results summarized in Table 3 show better overall performance for 'DA 1- 3 Overall results are summarized in Table 4, and presented for each site in Figures 6, 7, and 8.

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In those figures, the left column is related to the first soil layer, and the right column is  in Table 4).

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The convergence calculated for the Kendall site suggests that, overall, soil moisture is 6 constrained more effectively when observations of cosmic-ray neutrons are assimilated 7 into Noah (Figure 6g-i).For the first soil layer, total convergence levels are high in all 8 cases and little difference is observed between the two DA cases.The benefit of 9 assimilating observed neutron counts is more clear in the results for the second layer, with no substantial differences between the high-and low-frequency assimilation 11 strategies.However, the impact of higher retrieval frequency becomes evident in the 12 third soil layer in which soil moisture is only successfully constrained in the 'DA 1-hour'

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case. 14 The results from the Nebraska and Park Falls sites are comparable and they show  4).At Park Falls, the results from the deepest soil layer

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The convergence criterion computed for the first two soil layers in Noah at the Nebraska

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The first noticeable result from Figure 9 is that the average performance of Noah (i.e.,

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slightly worse at the deepest layer (Figure 9c).Surprisingly, a different pattern emerges

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from both the Nebraska and Park Falls sites where an initial period of frequent rainfall is 30 followed by a relatively long dry period which also starts in July (Figure 9d-i).In those

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"nearly-identical twin experiment" approach is adopted in which observations of cosmic-

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Summertime is characterized by an initial relatively dry period which lasts for about 2

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months followed by the monsoon.

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Unlike the results at Kendall, the comparison between 'DA 1-hour' and 'DA 2-day' for

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'optimal range' for integration of neutron counts for a specific site location but the 21 investigation is beyond the scope of this study.For example, our initial preliminary

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analysis indicated little difference between the 'DA 2-day' case with another assimilation 23 case where neutron measurements were assimilated daily.

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This study focused on the analysis using synthetic observations mainly because (1)

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there is a lack of independent soil moisture observations corresponding to similar

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The ensemble mean of the prior distribution is used for all ensemble simulations.

20 2005) 24 (
. The Park Falls/WLEF tower located in the Park Falls Ranger District of the 21 Chequamegon National Forest is characterized by a managed landscape where logging 22 activities such as thinning and clear-cuts are concentrated in the upland region (DAVIS 23 et al., 2003).The growing seasons are typically short and the winters long and cold Mackay et al., 2002).Soil moisture availability controls summer evapotranspiration at 25 the Kendall and Nebraska sites and to a lesser extent at the Park Falls (Teuling et al., 26 2009).

6 The
Noah used operationally at the National Centers for Environmental Prediction

13 deep 22 23 2 . 3
root zone layer, and a 1-m thick sub-root zone layer.The present study focuses on 14 the first three layers of the model where roots are prescribed to be present (0 to 1 m total 15 depth).Soil moisture parameterization is based on the one-dimensional Richards 16 equation (Chen et al., 1996; Ek, 2003).Soil and vegetation parameters were defined 17 from look-up tables and the Noah simulation run at hourly time steps at each selected 18 site.A full description of Noah can be found in (Chen and Dudhia, 2001) and in (Ek, 19 2003) and the model is available from the Research Applications Laboratory at the 20 National Center for Atmospheric Research (RAL/NCAR) at 21 http://www.ral.ucar.edu/research/land/technology/lsm.php.Cosmic-ray Soil Moisture Interaction Code (COSMIC) 24 In this study the COsmic-ray Soil Moisture Interaction Code (Shuttleworth et al., 2013) is 25 the forward observational operator used in data assimilation.COSMIC is characterized 26 by a simple, physically-based parameterization of belowground processes relevant for 27 soil moisture estimates using cosmic-ray sensors which includes (1) the degradation of 28 the incoming high-energy neutron flux with soil depth, (2) the production of fast neutrons 29 at given depth in the soil, and (3) the loss of the resulting fast neutrons before they reach 30 the soil surface.Despite its simplicity, COSMIC is robust and much more efficient than 31 the traditional Monte Carlo neutron particle model commonly employed in cosmic-ray 6

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Data assimilation combines the information from observations and model predictions in 8

18 general 22 N
filtering algorithm developed using Bayes Theorem (Wikle and Berliner, 2007), 19 and the method is described in detail by (Anderson, 2003) and (Anderson, 2009).The 20 probability distribution of a model state is approximated by an N-member sample of M-21 dimensional state vectors (x i ; i = 1, 2,…, N), where N is the ensemble size (in this study, = 40) and each x i is an M vector (e.g., soil moisture at each model layer).Because the 23 error distributions for observations taken at different times are usually assumed 24 independent in geophysical applications, each available observation can be assimilated 25 sequentially.Hence, for simplicity, the assimilation of a single scalar observation, y, is 26 used here.The Bayes Theorem is as follows: 11 et al., 2010).In order to avoid undesired instabilities at the beginning of the simulation, 12 no observation is assimilated during the first 24 hours.A schematic diagram of the 13 experimental setup is shown in Figure 3.14 We use these observations in our experiments to evaluate the ability of Noah to 15 reproduce the synthetically observed neutron intensity and consequently to analyze the 16 updated soil moisture profile against the 'true' soil moisture state.Notice that the neutron 17 intensity time-series produced in this study are not rescaled to correspond to the location 18 of the original COSMOS probe site in the San Pedro, as discussed by (Zreda et al.,

1 4. 1 Assimilation of neutron counts 2 For
all analyzed sites, the assimilation of summertime neutron observations in Noah 3 improves the dynamics relative to the true neutron count time-series in comparison with

11 ( 12 ((
monsoon) between July and early-September.Both the Nebraska and Park Falls sites Figure4b and 4c, respectively) show the opposite rainfall pattern with an initial period 13 with frequent rainfall (slightly more frequent at Park Falls) until about mid-June/early-14 July, followed by a relatively dry period for about 1-2 months (slightly longer at Park 15 Falls).Notice that 2012 was one of the driest years on record for the Midwestern USA 16 Blunden and Arndt, 2013).

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Both assimilation cases (i.e., with hourly-available observations -'DA 1-hour' shown as 18 the red line; and with observations available once every 2 days -'DA 2-day' shown as 19 green circles) suggest superior performance compared with the case without 20 assimilation (light blue line) (Table

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observe a tendency for lower spread values in comparison to RMSE at both sites for the 10 'DA 2-day' case.This tendency disappears when high-frequency observations are 11 assimilated (i.e., 'DA 1-hour') at the Park Falls site.For the Nebraska site, although still 12 present, the tendency is reduced for the 'DA 1-hour'.These results highlight the quality 13 of the OSSE carried out in this study as well as the distinct performance of the 14 assimilation system due to different timing in rainfall events occurred at all three 15 Ameriflux sites.

17 hour' 22 ( 24 4. 2 26 In
compared to 'DA 2-day', with both cases being almost always superior to the 'No 18 DA' case.In almost all cases, computed statistics with respect to the true counts are 19 better than those computed with the synthetic observations.This is expected because 20 an additional degree of randomness is introduced in the synthetic observations (i.e., light 21 gray circles in Figure4).The degree of improvement compares well with the results fromShuttleworth et al., 2013).23 Impact of near-surface cosmic-ray neutrons on simulated soil moisture 25 profiles the case of cosmic-ray sensors, the dynamics of equivalent neutron counts observed 27 can be assumed to be a proxy for integrated, depth-weighted variation of soil moisture at 28 sub-kilometer scales, as shown in(Shuttleworth et al., 2013).Here, we expand this 29 analysis by assessing how well all root zone layers in the Noah (prescribed as the first 30 one meter of soil in the model) are simulated with and without the assimilation of 31 observed neutron counts.The effective sensor depth computed from the synthetic observations at all three sites varies on average from ~12 cm during the wet period to 1 ~20 cm in the dry months.This corresponds to the entire surface (first) soil layer of Noah 2 with an additional contribution from the second soil layer in the model (10-40 cm layer).

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related to the deepest layer analyzed.The top row corresponds to the actual soil 7 moisture simulated by Noah for the three cases (i.e., 'no DA', 'DA 2-day', and 'DA 1-8 hour') in comparison to the true soil moisture state (same color-coding as before).The 9 middle row shows the difference between the Noah-derived and true soil moisture.We 10 selected an "uncertainty range" of ± 0.02 m 3 m -3 as our target for comparison which is 11 similar to the accuracy found in more traditional point-scale measurements (TOPP et al., 12 1980) and also comparable to the accuracy of cosmic-ray sensors (Franz et al., 2012a; 13 Rosolem et al., 2013).Note that the target accuracy from satellite remote sensing 14 products is twice as big, as discussed by (Brown et al., 2013; Entekhabi et al., 2010; 15 Kerr et al., 2010).The bottom row corresponds to a simple convergence criterion based 16 on the results from the middle row.For each hourly time step, we check whether the17difference with respect to the true soil moisture is within the "uncertainty range".If it is 18 within this range, the value is added to the current number of counts, and the percentage 19 convergence is taken with respect to the total number of points analyzed at that given 20 time.As an example, if the first point found within the "uncertainty range" is located in 21 position 50 of the time array, its convergence is computed as 2% (i.e., 1/50).If the next 22 time step is also within this range, its convergence is computed as ~3.9% (i.e., 2/51), 23 and so on.With this simple metric we can determine not only the overall percentage of 24 hours when the difference was within this uncertainty range (obtained at the end of the 25 simulation) but also how the convergence evolves as the simulation period progresses.26At the Kendall site, the results suggest overall improved performance of Noah for all soil 27 layers (including those beyond the sensor effective depth) when observed neutron 28 counts are assimilated regardless of the availability of observations (Figure6a-f).

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Differences between 'DA 1-hour' and 'DA 2-day' cases are larger at deeper soil layers 30 with 'DA 1-hour' showing superior performance.For the 'no DA' case, only the soil 31 moisture at the first layer in the model is within the uncertainty range for the majority of 32 the simulated period.The soil moisture for the 'DA 2-day' case compares relatively well 15 with the true soil moisture at the first two layers but estimated soil moisture in the third 1 layer is almost always outside of the uncertainty range.The 'DA 1-hour' case, however, 2 shows a remarkable response to neutron count and effectively simulates the soil 3 moisture dynamics at all Noah soil layers (basic statistics are calculated and presented 4

15 superior(
performance of Noah when assimilating neutron counts at high-frequency 16 Figures 7a-f and 8a-f).Surprisingly, for the first two soil layers in Noah the dynamics of 17 soil moisture obtained from the ensemble average for 'DA 2-day' is similar to the model 18 behavior for the 'no DA' case.In addition, 'no DA' soil moisture at the deepest analyzed 19 layer at the Nebraska site follows the true soil moisture states quite well.This is likely 20 related to the fact that the initial conditions randomly obtained in the model were already 21 similar to the true soil moisture state (in terms of ensemble averages) for the 'no DA' 22 case, although the overall magnitude of the spread is much larger compared to 23 assimilation cases (Table

24 analyzed
show superior performance of 'DA 1-hour' while 'no DA' and 'DA 2-day' have 25 similar dynamics especially after late-June.

27 and 1 Park
Park Falls sites (Figures7g-h and 8g-h) are slightly different from the results28discussed for the Kendall site (Figure6g-h).First, the percentage of points within the 29 uncertainty range at these two sites is greater than the percent values obtained at 30 Kendall (compare for instance, 'DA 1-hour' case across all sites).There is a much 31 sharper increase in the convergence criterion with time at these two sites as opposed to 32 the pattern observed for Kendall.However, unlike the Kendall site where the patterns of both DA cases were somewhat similar, it is much more clear for both the Nebraska and Falls cases that the 'DA 1-hour' is able to update soil moisture much more rapidly 2 than the 'DA 2-day' when compared to the response to the 'no DA' case.As mentioned 3 previously, the convergence results for the 'no DA' case at the third soil layer in the 4 model are likely to be related to the initial conditions from the ensemble mean being 5 already to close to the true states (Figures6i and 7i).

6 4. 3 Impact of retrieval frequency on simulated soil moisture dynamics 7 18 Figure 9
Figure 9 with top, middle, and bottom rows corresponding, respectively to the Kendall,

23 using the 2 -
day time windows) when trying to simulate true soil moisture profiles is best 24 when neutron measurements are assimilated at hourly timescales (i.e., 'DA 1-hour') at 25 all sites.At the Kendall site, which is characterized by a long dry period followed by the 26 monsoon onset early in July, the performance of Noah for the 'DA 2-day' case is similar 27 to that obtained with 'DA 1-hour' at the first two layers of the model (Figure 9a-b), and

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Summary and conclusions 16The use of cosmic-ray neutron sensors for soil moisture monitoring has been fast 17 growing because the technique provides root-zone soil moisture estimates at 18 unprecedented spatial scales and at high temporal resolution.This paper evaluates the 19 ability of a land surface model to translate the information obtained from cosmic-ray 20 neutrons observed aboveground into soil moisture estimates for individual soil layers.A

22 ray
neutrons were generated from the land surface model with a slightly different model 23 configuration (perturbed key soil and vegetation parameters).Below we discuss the 24 implications and summarize the main findings of this work.25Howeffectively is the information from aboveground cosmic-ray neutrons translated to 26 individual soil moisture layers in the model?27Whenassimilating neutron counts at high frequency, the performance of the land 28 surface model is remarkably improved in comparison with the soil moisture profiles 29 simulated without data assimilation.This finding is observed for all three biomes with 30 degree of improvement varying slightly from site-to-site.Of importance, we found that 31 water in the soil is better estimated at depths well below the effective sensor depth and encompassing the entire rooting zone in the model.Therefore, the high observational 1 frequency of the cosmic-ray sensors can potentially introduce additional benefits relative 2 to assimilating local/regional soil moisture observations from satellite remote sensing 3 products available at coarser temporal resolution.However, care must be taken when 4 accounting for measurement uncertainty by removing any potential signal in the 5 measurement from other sources of hydrogen (atmospheric water vapor, water in 6 biomass), hence isolating or maximizing the soil moisture information content in the 7 measurement.Another important aspect is to ensure sufficient ensemble spread from 8 the model to avoid, for instance, filter divergence (over-confidence in the model), or 9 alternatively directly inserting observations with little or no model influence (over-10 confidence in the observations) (Anderson, 2007; Hamill et al., 2001; Houtekamer and 11 Mitchell, 1998).12How does frequency of available observations of cosmic-ray neutrons influence model 13 performance?14 We use the RMSE calculated for every 2-day time-window as a metric for model 15 performance.At the Kendall site, 'DA 1-hour' and 'DA 2-day' showed good agreement 16 for soil moisture in the first two layers of the model (0-10 and 10-40 cm).However, the 17 benefits of high-frequency retrievals in the case of cosmic-ray neutron observations is 18 also observed for the third soil layer in Noah (40-100 cm), where 'DA 1-hour' is much 19 superior to 'DA 2-day'.Particularly to the Noah, the distribution of roots is directly 20 proportional to the thickness of each soil layer.Therefore, the third layer of the model 21 plays a significant role in determining evapotranspiration rates at the surface.

25(
Nebraska and Park Falls suggest that the performance of Noah for the 'DA 1-hour' case 26 is always superior to that from 'DA 2-day' in all soil layers analyzed.Surprisingly, the 27 model performance for the 'DA 2-day' case is not much different from simulations made 28 without assimilating cosmic-ray neutron counts (i.e., 'no DA' case).A distinct 29 characteristic from both the Nebraska and Park Falls sites in comparison to Kendall is 30 the overall dynamics of soil water in the summertime.At Nebraska and Park Falls, a 31 relatively wet period with frequent rainfall is observed at the beginning of the 32 summertime period, lasting for about 2 months, and followed by a relatively dry period with low or no rainfall.Overall, the benefits of assimilating neutron measurements at 1 relatively higher frequency are more clearly observed at the Nebraska and Park Falls 2 sites relative to the semi-arid Kendall.This could indicate that the assimilation 3 performance of summertime cosmic-ray measurements at high temporal resolution may 4 depend not only on heterogeneity of soil properties (accounted for by slightly perturbing 5 model parameter from true soil moisture states) but also slightly on meteorological 6 forcing and its climatology (namely, rainfall).Also, these findings suggest an important 7 role of high-frequency measurements to better constrain soil moisture states simulated 8 by hydrometeorological models when applied to drought monitoring given that the 9 summer of 2012 was one of the driest on record in the Midwestern USA region.10 Due to the characteristics of the sensor, the integration time used to compute neutron 11 intensity should potentially be longer than one hour at some locations.In practice, this is 12 done to reduce the uncertainty in the measurement and consequently ensure an 13 accurate estimate of soil moisture.For instance, neutron count rates integrated over the 14 entire day were used in a humid forest ecosystem located in western of Germany 15 because hourly count rates were too low for accurate soil moisture measurements 16 Bogena et al., 2013).The results presented in our study show that care must be taken 17 when integrating the cosmic-ray measurements over a longer-period while combining 18 with models, suggesting a potential trade-off between individual sensor accuracy and 19 successful representation of soil moisture profile dynamics.This could imply in an

1 Figure 1 .
Figure 1.Schematic representation of the effective measurement volume for the cosmic-ray soil moisture sensor.The effective depth

Figure 2 . 2 (
Figure 2. Schematic representation of the data assimilation and state update procedures in the Data Assimilation Research Testbed

1 Figure 3 .
Figure 3. Experimental setup used in this study for data assimilation of synthetic observations of cosmic-ray neutrons.

2 1 Figure 4 .
Figure 4. Equivalent neutron intensity (counts per hour -cph) simulated by Noah coupled to COSMIC without (no DA) and with data

1 Figure 6 .
Figure 6.Comparison of soil moisture dynamics at the Kendall site for the first three soil layers in Noah.Top row: Simulated soil

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Results show actual model time steps (i.e., hourly).The ensemble mean of the prior distribution is shown for all ensemble 6 simulations.

Figure 9 .
Figure 9.Comparison of Noah performance in representing soil moisture dynamics for the first three soil layers with respect to the Soil layer 40-100 cm ; Houtekamer and 14 Mitchell, 1998).In the hydrometeorological community interest in ensemble data 15 assimilation methods is growing rapidly for flood forecasting (Clark et al., 2008) and soil 16 moisture applications (e.g., (Draper et al., 2012; Kumar et al., 2012; Li et al., 2012).

Perturbed meteorological forcing and initial conditions 11
In order to ensure appropriate ensemble spread throughout the assimilation procedure, 12 time series of cross-correlated perturbation fields were generated for all meteorological 13 forcing inputs from Noah and applied to each individual ensemble member (total of 40 14 members), similar to the approach used by (Shuttleworth et al.simplicity, defined always at noon GMT).The 2-day frequency was selected because it 9 is similar to the temporal resolution likely to be achieved by the most recent satellite 10 remote sensing soil moisture missions (Brown et al., 2013; Entekhabi et al., 2010; Kerr 12observations, one would like the RMSE (which represents the accuracy of the ensemble 1 mean state relative to the observations) to be comparable to the total spread (which 2 contains both the ensemble spread and observational error signals).In that case, the 3 RMSE is defined as the square root of the average squared difference between the 10Figure5shows the comparison between the RMSE (black circles) and spread (red 11 diamonds) for all analyzed cases at all sites.Overall, the magnitudes for the spread 12 compare well with the ones for RMSE suggesting that this is a successful assimilation 13 experiment.Notice that these two quantities tend to be closest to each other for the 'DA 14 1-hour' case (right column) and the largest differences are seen for the 'No DA' case (left 15 column).The rapid reduction in total spread at the Kendall site with time for the 'No DA' 16 case is due to the fact that soil moisture presents a strong 'damping' signal, especially in 17 the first few months when little rainfall occurs (May-July).This is fundamentally the same 18 behavior observed when models are 'spun-up' or 'warmed-up' for a selected period of 19 time prior to their final analysis simulation.Consequently, individual ensemble members 20 move towards a preferred state.Notice that this behavior is not clearly observed at the 21 Nebraska and Park Falls site where rainfall occurs continuously in the first months (May-22 July).In comparison to the 'No DA' case, RMSE for both assimilation cases are reduced, 23 with the lowest RMSE values found for the 'DA -1hour' case.
Unlike the 'DA 1-hour' case, the 'DA 2-day' case allows for Noah to freely 1 advance in time for the rest of the 2-day period once it has assimilated the neutron count 2 measurement, and because the true simulation was generated with a different set of 3 parameters than the cases analyzed here, model simulations in the 'DA 2-day' case are 31cases, the performance of 'DA 2-day' is not improved substantially in comparison to 'no ceases in July.while also depending on model uncertainties due to lack of representativeness of key 11 soil and vegetation properties at the scale of interest (here, accounted for by the fact that 12 true soil moisture is generated from a model simulation obtained with slightly perturbed 13 parameter values).
20and litter layer, carbohydrates of soil organic matter and belowground biomass (Bogena 1 et al., 2013).For instance, changes in biomass over time may become important 2 especially at the Nebraska (cropland) site.However, as with any OSSE, there are some 3 limitations in our approach because the uncertainties due to the above-mentioned (Shuttleworth et al., 2013)13)).Typical sources include surface water (Franz et al., 32 2012a), atmospheric water vapor (Rosolem et al., 2013), biomass (Franz et al., 2013b),

2 3 Table 1 .
Site information obtained from Ameriflux database (http://ameriflux.lbl.gov).MAT = Mean Annual Temperature, and MAP = Mean Annual Precipitation.Notice the 2 analyzed period in this study is a subset of the available data from each site and it is Date/time format as follows YYYY-MM-DD_HH, where YYYY is the year, MM is the 5 month, DD is the day of the month, and HH is the hour in GMT. *

Table 3 .
Summary of statistics computed for Noah for assimilation of synthetic neutron 1 intensity measurements in counts per hour (cph).Metrics are computed with respect to 2 both true counts and synthetic observations, respectively 'w.r.t.True' and 'w.r.t.Obs'.

Table 4 .
Summary of statistics computed for Noah for assimilation of synthetic neutron intensity measurements for all sites.All 1 metrics are calculated only when individual layer convergence is above 40% for the case 'DA 1-hour' (see bottom panel of Figures 6,27, and 8), and with respect to the true soil moisture state.The ensemble mean of the prior distribution is used for all ensemble 3 simulations.Numerical values are rounded to the first three decimal points.
Figure 5. Root-Mean-Squared-Error (RMSE) calculated for the ensemble mean relative to the 'true' observations (black circles) in 2 comparison to the ensemble spread (red diamonds).The ensemble mean of the prior distribution is used for all ensemble