Atmospheric moisture content is critical in hydrological modeling yet is sparsely measured in mountainous environments. We compared densely distributed measurements of dew point temperature in two study sites in the Sierra Nevada, California, against (1) simple empirical algorithms, (2) the Parameter-elevation Regressions on Independent Slopes Model (PRISM), (3) radiosonde data, and (4) the Weather Research and Forecasting (WRF) mesoscale model. Empirical algorithms that used only one sea-level measurement of dew point to extrapolate to higher elevations often did not match local dew point lapse rates and could be biased as high as 9.9°C. PRISM improved upon these methods by using local observations to determine the local average dew point lapse rate, with median bias values of −0.3°C and 3.3°C in our two study sites. Empirical algorithms that derived dew point from air temperature showed a seasonal variation in performance; summer median bias values were 0.6°C–8.2°C wetter than winter bias values. Radiosonde readings showed median biases of −6.5°C and −8.0°C from observations in our study sites. WRF improved on the radiosonde data, performing well in representing both the overall trends in the basin (with median biases of −0.9°C and −1.0°C in our study sites). One base station within the basin paired with PRISM lapse rates showed small biases from overall moisture trends. However, a physically resolved model such as WRF was better equipped to represent daily dew point variations and in basins with nonlinear trends.
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 Atmospheric moisture content, typically measured as dew point temperature or relative humidity (RH), is a critical factor in modeling both the energy and water balances in a river basin. Atmospheric moisture affects the energy balance by influencing both incoming longwave radiation and latent heat transfer [Ruckstuhl et al., 2007]. Longwave radiation, which is infrequently measured, is often estimated with algorithms which rely on air temperature and water vapor in the atmosphere [Flerchinger et al., 2009]. Because increased water vapor raises the emissivity of the earth's atmosphere, higher dew point values increase incoming longwave radiation at the surface [Rangwala et al., 2009]. Dew point measurements are particularly important in making accurate empirical estimates of longwave radiation when clouds are present, due to increased atmospheric emissivity [Sicart et al., 2006]. At the same time, a smaller difference between the air temperature and the dew point temperature (dew point depression) results in reduced evaporation or sublimation and thus less surface cooling due to latent heat. Inaccurate longwave radiation and energy balance estimates can change the modeled timing of snowmelt and the estimated energy available for potential evapotranspiration (ET), affecting the projected water balance for agricultural and urban uses.
 Dew point depression also affects the water balance by changing the amount of water evaporated or transpired from a basin. ET increases with a greater dew point depression, as there is a greater deficit between the moisture that the atmosphere can hold and the current moisture content. The Penman-Monteith equation, which can be used to estimate ET, is sensitive to changes in dew point depression, as well as being influenced by the estimated longwave radiation [Gong et al., 2006].
 Despite its importance to hydrology, atmospheric moisture is sparsely measured. Data limitations are exacerbated at higher elevations in complex terrain [Lundquist et al., 2003]. Of the available mountain meteorology network stations, only a small fraction record atmospheric moisture variables. For example, in the Snow Telemetry (SNOTEL) network, a system of high elevation weather stations maintained by the National Resources Conservation Service for water supply and snowmelt, only about 15% of over 800 stations around the western U.S. measure relative humidity (http://www.wcc.nrcs.usda.gov/snow/; accessed 1 September 2012).
 Given limited measurements, numerous empirical algorithms have been developed for projecting dew point temperatures or RH across mountainous terrain. These range in complexity from simple extrapolations to more extensive calculations that require iterative schemes. In general, these empirical algorithms fall in two categories: (1) no measurements are available in a watershed [Kimball et al., 1997; Running et al., 1987], and (2) only one point measurement is available, which must be distributed across a basin [Cramer, 1961; Franklin, 1983; Kunkel, 1989; Wigmosta et al., 1994]. Most of the algorithms available were developed in continental regions, such as western Montana [Running et al., 1987], New Mexico, and Texas [Kunkel, 1989]. Kimball et al.  notes that algorithms developed in arid locations have limited accuracy in regions outside where they were developed. For example, Waichler and Wigmosta  found that when generating meteorological data in the Oregon Cascades, using the minimum temperature for daily dew point did not match the observed RH pattern as well as using historical observations of monthly and hourly RH means. Eccel  found that while the widely used methods [Kimball et al., 1997; Running et al., 1987] were appropriate in the Italian alps, site-specific calibrations based on time of the year and presence of precipitation were required.
 Furthermore, our future ability to rely on relations determined empirically from historical observations will be limited by changes in atmospheric moisture. Dew point temperatures have increased by several tenths of a degree per decade across most regions of the United States during 1961–1995, reflecting an increase in atmospheric water vapor [Gaffen and Ross, 1999; Robinson, 2000; Trenberth et al., 2007]. While relative humidity trends are weaker, these reflect increases across the country as well [Gaffen and Ross, 1999]. Climate model projections indicate that the water vapor content of the atmosphere will continue to increase in the future [Dai et al., 2001; Trenberth et al., 2007].
 Given the importance of atmospheric moisture content in hydrological modeling and the sparsity of measurements in mountain locations, here we investigate options for representing dew point temperatures across gradients of elevation in two basins in the Sierra Nevada. The Sierra Nevada is of particular concern to water resource managers, as there are significant future water supply shortages projected in this region [Barnett, et al., 2008]. Furthermore, the Sierra Nevada is in a semiarid climate, according to the updated Köppen–Geiger climate classification [Peel et al., 2007], and provides a geographic barrier between maritime influences to the west and deserts to the east.
 To understand different measures of atmospheric moisture content and how they change in complex terrain, we first review the relevant atmospheric variables (section 'Background: Metrics of Atmospheric Water Content'). We next present the study areas and data sources used (section 'Study Area and Data Sources'). We present a summary of methods to estimate dew point temperatures in a mountain basin when limited or no observations are available (section 'Methods of Estimating Dew Point Temperatures'). These include (a) simple empirical algorithms, (b) the Parameter-elevation Regressions on Independent Slopes Model (PRISM), which uses local lapse rates based on observations [Daly et al., 2008], (c) the basic atmospheric structure as seen in data from a nearby radiosonde sounding, and (d) the Weather Research and Forecasting (WRF) model, which is a numerical weather prediction system informed by surface and upper-air measurements [Michalakes et al., 2001]. These methods were selected to test the transferability of empirical fits to our study site (empirical methods), including whether physical principles of conservation of moisture in a lifted air mass are an appropriate metric for these basins. Additionally, we test whether the assumption of uniform advection of the free atmosphere describes moisture dynamics in the mountain range (radiosonde data), or whether a full atmospheric physics model is necessary to capture dew point variations (WRF). Methodology includes a summary of analysis techniques (section 'Techniques for Assessing Observed Dew Point Patterns') and a hydrological model used to illustrate the impacts of dew point estimation errors (section 'Hydrologic Model'). The results (section 'Results') first summarize with a case study (section 'Case Study of Estimated Dew Point Temperatures in the Sierra Nevada') and then evaluate the performance of these models in representing atmospheric moisture in the study sites (section 'Overall Performance of Methods of Generating Dew Point Temperatures') and the factors affecting their performance (section 'Factors That Affect Estimation of Dew Point Temperatures in the Sierra Nevada'). We illustrate the impacts of errors in representing atmospheric moisture on timing of snowmelt and quantity of streamflow (section 'Impacts on Hydrology') and conclude with guidelines for choosing methods to represent atmospheric moisture content in the Sierra Nevada and similar mountain regions.
2. Background: Metrics of Atmospheric Water Content
 Atmospheric moisture content is influenced by the air temperature and the local atmospheric pressure, which change with elevation according to the ideal gas law. Atmospheric moisture content may be expressed in several ways. The mixing ratio (R) defines the mass of water in the atmosphere per kilogram of dry air. The actual vapor pressure of water (Ea) defines the amount of water in the air in units of pressure, while the saturation vapor pressure (Esat) is the amount of water that the air can hold at a given temperature. The relative humidity (RH) is the ratio of the actual vapor pressure over the saturation vapor pressure. The dew point temperature (TD) is the temperature at which the air will be saturated for a given amount of water vapor. The difference between the actual air temperature and dew point temperature is termed the dew point depression. Further explanations on these variables and how they can be calculated are provided in Appendix Atmospheric Moisture Metrics and Calculations.
 Figure 1 illustrates relations between measures of atmospheric moisture below the condensation level when holding dew point temperature or relative humidity constant with changes in elevation. In Figure 1a, we show cups of water to visualize atmospheric moisture (figure adapted from Cramer ). The size of the cup is the potential amount of water that the air can hold at a given temperature. As elevation increases, temperature decreases, in turn decreasing the overall size of the cup. The amount of moisture in the air is represented by the water in the cup. Figure 1b shows dew point temperature (TD), mixing ratio (R), actual vapor pressure (Ea), and relative humidity (RH) with changes in elevation. When dew point temperature is held constant with elevation, water vapor pressure remains constant, while RH increases due to decreasing air temperature, and the mixing ratio increases due to pressure changes with elevation. A constant mixing ratio with changes in elevation is similar to constant dew point temperature, except that due to pressure changes with elevation, vapor pressure and dew point temperatures decline slightly. When RH is held constant with elevation, the dew point temperature, mixing ratio, and actual water vapor decrease with elevation.
 For this study, we represent atmospheric moisture with dew point temperature. We choose this representation for three reasons. First, dew point temperature is familiar to water resource managers as the most commonly used humidity measure [Gaffen and Ross, 1999; Robinson, 1998] and is the metric used in numerous models [Daly et al., 2008; Kimball et al., 1997; Running et al., 1987]. Quality control techniques used for air temperature can be applied easily to dew point temperature. Second, dew point temperature most frequently shows a clear linear variation with elevation. Third, dew point is a conservative property with isobaric heating and cooling as long as water does not condense or evaporate, and thus represents the physical amount of moisture in the air [Glickman, 2000].
3.1. Study Area and Data Sources
 We assessed the performance of methods of estimating dew point temperature at two well-instrumented study sites located on the west slope of the Sierra Nevada, California, to represent two cases of topographic controls. These sites are the North Fork American River Basin (ARB), where elevation increases fairly uniformly from west to east, and the Yosemite area, which contains multiple subbasins that experience cold-air pooling effects and deviations from linear air temperature lapse rates [Lundquist and Cayan, 2007; Lundquist et al., 2008] (Figure 2). The Sierra Nevada receives the majority of its precipitation in the winter and early spring and little during the summer. Annual precipitation and runoff can fluctuate between 50% and 200% of the climatological averages [Lundquist and Cayan, 2007]. In the Sierra Nevada, water vapor contributions are from the Pacific Ocean for most of the year [Dodd, 1965; Robinson, 1998]. On a coarse scale, dew point temperatures decrease between Sacramento (5 m) and high elevations (1600 m) in the Sierra Nevada [Dodd, 1965]. Orographic effects result in drier air on the east slope of the Sierra Nevada. Average temperatures range from 1°C in the ARB and −2°C in Yosemite during December, to 17°C in both sites in July. Average dew point temperatures range from −4°C in the ARB and −9°C in Yosemite in December, to 5°C in the ARB and 4°C in Yosemite in July.
 In the ARB, we used data from water years 2008 to 2010 (a water year is defined as October of the previous year through September of the current year) from permanent meteorological towers and hygrochron iButtons (http://www.maxim-ic.com/datasheet/index.mvp/id/4379; Table 1 and Figure 2a). Permanent meteorological towers from elevations between 7 and 2100 m in the ARB were part of the NOAA Hydrometeorology Testbed (HMT; http://hmt.noaa.gov). The HMT is a meteorological measurement program aimed at providing data for improved hydrologic forecasting [Ralph et al., 2005], with measurements sampled every 2 min. These stations provided air temperature and relative humidity data from HMP45 sensors and precipitation data from a combination of tipping bucket and weighing gauges. A dense measurement network was created with hygrochron sensors, a stand-alone device that measures air temperature and RH and records the data in an enclosed data logger with an accuracy of 5% RH (see supporting information for hygrochron evaluation, including use in trees, and programming specifications). Hygrochrons were installed in evergreen trees 1.5–4 m above the ground (depending on average local snow depth) and shielded from rain, snow, and solar radiation with upside-down plastic funnels. Deployment methodology followed Lundquist and Huggett , with evergreen branches providing further radiative shielding. The hygrochrons were deployed for water years 2008–2010, although the precise locations with working sensors varied by water year. These changes introduced negligible interannual variations in dew point temperature lapse rates. On average, 35 hygrochrons were deployed each water year over the study period, representing 64 locations that ranged in elevation from 424 to 2429 m.
Table 1. Observational Data
Period of Record (Water Years)
Count of Stations
Elevation Range (m)
Hydrometeorological Testbed Stations
 In Yosemite, we used data from permanent meteorological towers and Hobo sensors (http://www.onsetcomp.com/products/hobo-data-loggers; Table 1 and Figure 2b). These data run an east-west transect crossing the Merced and Tuolumne River basins up to the ridge line of the Sierra Nevada. Data from permanent meteorological towers at elevations from 311 to 3031 m were acquired from the California Department of Water Resources Data Exchange Center (CDEC), a hydrometeorological data program in California originally started for flood forecasting (http://cdec.water.ca.gov/intro.html). The CDEC stations provided hourly air temperature and relative humidity data from Handar 442 sensors and precipitation data from weighing gauges. Hobo sensors were deployed during May or June for 1–2 years at a time for water years 2003–2005, recording data every 15–30 min [Lundquist et al., 2003] with an accuracy of 2.5% RH. An average of 20 Hobo sensors were deployed each water year over the study period, representing 25 locations that ranged in elevation from 1309 to 3205 m up the west slope of the Yosemite study site. All data were quality controlled using the methodology of Meek and Hatfield . This included removing extreme spikes in the data, values outside of the threshold of operation, and long periods of constant data records that were not consistent with nearby stations in the basin. For analysis, data were averaged into daily-averaged and monthly-averaged time series. (Observations from both the ARB and Yosemite data sets are provided in the supporting information.)
3.2. Methods of Estimating Dew Point Temperatures
3.2.1. Empirical Algorithms: Projecting Dew Point From a Base Station
 Where a single point measurement of moisture content exists, empirical algorithms use data from a base station and make assumptions about the variation of moisture across an elevation gradient to project dew point temperatures to sites in the basin. The following algorithms can be used to spatially extrapolate moisture content (Table 2). Cramer , based on a study in western Oregon, assumes thorough mixing between air layers, which results in a constant mixing ratio (and thus atmospheric water content) with elevation. The mixing ratio is conserved during adiabatic lifting of an air parcel [Wallace and Hobbs, 2006], so we would expect this relationship if topographically forced air movement is the primary cause of vertical variation in meteorological conditions, and no moisture condensation is occurring. Franklin  used observations from the Priest River Experimental Forest in northern Idaho and found that dew point temperature varies with elevation according to a lapse rate of −1.25°C km−1, which is very close to the lapse rate expected from a constant mixing ratio as in Cramer . Kunkel  extrapolates water vapor pressure based on an exponential relation of the difference between site elevation and base station elevation. This is corrected with monthly varying coefficients empirically calculated from 11 stations in the intermountain west; data were from the climate atlas of the United States [National Oceanic and Atmospheric Administration, 1968]. This algorithm thus fits a seasonally varying empirical adjustment to declining water vapor pressure with elevation. Some hydrologic models, such as the Distributed Hydrology Soils and Vegetation Model (DHSVM), assume a constant relative humidity throughout a basin when only one input station is used [Wigmosta et al., 1994]; given that temperature decreases with elevation, this would imply that moisture declines with elevation. This assumption will be referred to as “constant RH” throughout the paper. Note that when multiple input stations are supplied to the DHSVM, the user can select an interpolation scheme for RH data between the stations; we assumed the case of one base station. Franklin  is cited as the lapse rate of choice in the Mt-Clim meteorology model [Running et al., 1987]. SnowModel [Liston and Elder, 2006], a snow evolution model, employs the Kunkel  method for relative humidity extrapolations.
Table 2. Empirical Algorithms: Spatial Projections of Dew Point Measured at a Base Stationa
One dew point measurement available. Citation count acquired from Google Scholar, 4/9/12.
DHSVM is employed widely. RH distribution is included in the hydrologic model
Relative humidity is constant throughout the basin if only one input station is used in the hydrologic model. If multiple stations are used, RH is interpolated between stations.
 When utilizing empirical algorithms that project dew point temperatures from a base station, we must consider the following: (a) how well does the modeled lapse rate fit the observed lapse rate, including whether there is a consistent linearity of dew point temperature variation with height and (b) how much does the location of the base station influence modeled results. The choice of base station from which to project dew point temperatures may be limited; often the only reliable source available is a low-elevation airport weather station. To investigate the performance of projecting dew point temperatures given standard available data, dew point temperatures were extrapolated from the Sacramento International Airport weather station to observation locations within the ARB and from the Fresno International Airport weather station to observation locations within Yosemite (Figure 2).
3.2.2. Dew Point Temperature Lapse Rates From Local Data: PRISM
 The PRISM creates gridded data sets of climate parameters using the procedures described by Daly et al. . Observations are used in linear regressions to define local lapse rates and construct grids. Available stations are weighted according to their similarity to their local grid cell with adjustments for topographic blocking. Digital maps at a resolution of 4 km are available for average dew point data on monthly and annual timescales (http://prism.oregonstate.edu/). This technique is similar to the empirical methods based on one atmospheric moisture measurement in a basin, except that this regression is based on all available local observations. We acquired dew point temperatures for grid cells in the Yosemite area for water years 2003–2005 and the ARB for water years 2008–2010 and did a nearest neighbor comparison to all observations located within the grid cells.
3.2.3. Empirical Algorithms: Estimating Dew Point From Air Temperature Alone
 When no atmospheric moisture measurements exist, empirical algorithms may use air temperature to estimate water vapor measurements (methods described in Table 3). The methods of Running et al. , developed primarily in Montana but employed widely across the United States, use the daily minimum temperature as the dew point temperature. This assumes that dew forms every night, and given the latent heat released by condensation, the air temperature does not drop below the dew point temperature. Kimball et al.  note that the minimum nighttime temperature may be higher than the dew point temperature in arid climates, where dew may not form every night. Their algorithm, validated at stations across the United States, expands upon the Running et al.  method by adjusting the calculated dew point depending on the aridity of the region, as measured by the ratio of the daily potential ET to annual precipitation. To investigate performance of these algorithms, we compared the local measured dew point with that estimated from colocated air temperature measurements at each study site location.
Table 3. Empirical Algorithms: Based On Air Temperaturea
No atmospheric moisture measurements in a basin. Citation count acquired from Google Scholar, 4/9/12.
Validated at 52 weather stations in the continental United States from 1987 to 1994
Calculates dew point (TD) from min (Tmin) and max (Tmax) daily temperature and the ratio of daily PET to annual precipitation (EF; in Mt-Clim, effective annual precipitation is generated from 3 month moving window).
 Many hydrologic models estimate dew point temperature from air temperature. The Mt-Clim meteorological preprocessing model [Glassy and Running, 1994; Kimball et al., 1997], which is used for the widely applied variable infiltration capacity (VIC) hydrologic model [Liang et al., 1994], the RHESSys hydroecological model (Regional Hydro-Ecologic Simulation System) [Tague and Band, 2004], and the Advanced Weather Generator meteorological preprocessor [Ivanov et al., 2007] for the Real-Time Integrated Basin Simulator (RIBS) [Ivanov et al., 2004], employs methods from the Running et al.  and Kimball et al.  algorithms. The VIC preprocessor methods were applied to generate the widely used Maurer et al.  and Hamlet and Lettenmaier  atmospheric forcing data sets for hydrologic modeling.
3.2.4. Free-Air Variations: Radiosonde Data
 Radiosonde balloon data (RAOB) inform the boundary conditions for the WRF atmospheric model [Mesinger et al., 2006]. To test if uniform advection of the free atmosphere conditions can represent dew point temperatures in the basin, free-air dew point data were acquired from radiosonde weather balloon measurements at Oakland (Figure 2), obtained from the NOAA radiosonde database (http://www.esrl.noaa.gov/raobs/). Sounding data were available twice daily, at 00 and 12 UTC (1600 and 0400 PST). These data were averaged daily and interpolated to the elevation of observations in the ARB and Yosemite.
3.2.5. Mesoscale Atmospheric Model: WRF
 The WRF model is a physically based numerical weather prediction model [Skamarock and Klemp, 2008]. An advantage of WRF is that it is internally consistent: physical relations between air temperatures and dew point temperatures are maintained, which may not be true in some empirical formulations. For this study, initial and lateral boundary conditions in the WRF product were forced with the 32 km gridded North American Regional Reanalysis (NARR), a meteorological product that incorporates surface and upper-air observations over the continental United States [Mesinger et al., 2006]. The WRF model resolves vertical temperature and moisture profiles using the YonSei University (YSU) boundary layer scheme [Hong et al., 2006], the Morrison two-moment microphysics scheme [Morrison et al., 2009], the rapid radiative transfer model longwave radiation scheme [Mlawer et al., 1997], the Dudhia  shortwave radiation scheme, and the Noah land surface model with four ground layers [Chen and Dudhia, 2001]. Snow and soil conditions were reinitialized to the NARR values every 5 days; in between WRF freely evolved and modified these values. To test the ability of WRF to represent spatial gradients of atmospheric moisture, the WRF model was dynamically downscaled to a 6 km resolution of a subsection of California, as described by Hughes et al.  and Wayand et al. . Hourly outputs of 2 m near-surface vapor pressure and temperature were acquired for October-June of water years 2001–2010 for 6 km grid cells within the Yosemite area and ARB and converted to dew point temperatures following equations in Appendix Atmospheric Moisture Metrics and Calculations. We did a nearest neighbor comparison to all observations located within the grid cells to assess the performance of the model.
3.3. Techniques for Assessing Observed Dew Point Patterns
 We evaluated observed dew point temperature patterns and concurrent meteorology to identify reasons behind the performance of the models. To assess the presence of a linear dew point lapse rate, we calculated a best fit line between daily dew point temperatures and elevation. The root-mean-square error (RMSE) between observations and this best fit line defines the amount of scatter from a linear lapse rate, where a low RMSE indicates a relatively linear dew point lapse rate with elevation, while a high RMSE shows scatter in dew point temperatures with elevation.
 To assess the impact of precipitation on dew point model performance, we considered days with rain to be those where precipitation measured at centrally located permanent stations within the basins (the Alta HMT station in the ARB and the Tuolumne Meadows CDEC station in the Yosemite area) was greater than zero, while dry days were days in which no rain was recorded.
 The influence of wind patterns was considered using the NOAA NCEP/NCAR reanalysis data sets (National Centers for Environmental Protection/National Center for Atmospheric Research, http://www.esrl.noaa.gov/psd/data/composites/day/; accessed 27 July 2012). These can be used to build composite data sets to analyze large-scale meteorological patterns. Vector wind composites were created at the 850 and 700 mb geopotential levels to illuminate wind patterns affecting the ARB and Yosemite areas, respectively. These composites were created for vector wind averages over all days with linear dew point temperature RMSE values of <1°C, 1°C–2°C, or >3°C.
3.4. Hydrologic Model
 The propagation of dew point estimation errors in hydrological modeling is illustrated using the DHSVM in a small basin in the Yosemite area, the upper Tuolumne River Basin (186 km2) above Tuolumne Meadows, ranging between 2600 and 4000 m elevation (Figure 2b). DHSVM is a physically based distributed hydrology model that requires inputs of air temperature, relative humidity, wind speed, and incoming shortwave and longwave radiation and precipitation [Wigmosta et al., 1994]. The input relative humidity is assumed constant over the basin when only one base station is supplied. The model was calibrated for water years 2003–2009 [Cristea et al., 2013] and run at a 3 h time step, with a 150 m grid spacing. Temperature, relative humidity, incoming shortwave radiation, and wind speed were measured at the Dana Meadows snow pillow site at 2966 m elevation. Temperature was distributed with a constant lapse rate of −6.5°C km−1. Wind speed and relative humidity were distributed uniformly through the basin. Incoming shortwave radiation was distributed using solar geometry calculations that were corrected for terrain shading effects [Wigmosta et al., 1994]. Incoming longwave radiation input data were calculated using the Idso  algorithm for clear sky conditions and distributed uniformly across the basin. Baseline dew point temperatures were calculated using the measured temperature and relative humidity data. These were then adjusted to represent uniform biases of ±2°C in dew point temperature. When a positive bias caused the dew point to exceed the air temperature, the dew point temperature was capped at the air temperature (to prevent unphysical conditions of supersaturation). Given that the intent was to model only the effects of biases in atmospheric moisture, we selected not to increase the air temperature in the basin along with the dew point, as that would impact modeled results, mainly through warmer air temperatures accelerating snowmelt. This was necessary in 15% of the total time steps, resulting in an average dew point temperature increase of 1.85°C. ET, latent heat fluxes, streamflow, and snow water equivalent (SWE) generated by the model were compared to values using locally measured (baseline) dew point data. Sublimation rates were approximated from latent heat fluxes over the snowpack at Dana Meadows, using the latent heat of sublimation.
4.1. Case Study of Estimated Dew Point Temperatures in the Sierra Nevada
 We illustrate the performance of methods of estimating dew point data in the ARB (Figure 3) and Yosemite (Figure 4). Here we show modeled dew point temperatures plotted against elevation. In both basins 2 days are shown, 1 day (left column) with a strong linear trend between dew point temperature and elevation, where better performance of the algorithms is expected, and 1 day (right column) with a weak trend between dew point temperatures and elevation. In both sites, the day with a strong linear trend is experiencing a high pressure gradient off the Pacific Ocean, indicating strong westerly winds, while the day with a weaker trend shows a high-pressure zone over the mountains in the ARB and a northward pressure gradient in Yosemite, indicating weak winds.
 Methods of representing dew point temperatures include lapse rate assumptions (Figures 3a, 3b, 4a, and 4b), algorithms based on air temperature (Figures 3c, 3d, 4c, and 4d), and methods based on free-air data (Figures 3e, 3f, 4e, and 4f). Both the assumptions of a constant mixing ratio with elevation [Cramer, 1961] and of the almost equivalent −1.25°C km−1 lapse rate [Franklin, 1983] do not lose moisture quickly enough with gains in elevation. Adjustments to vapor pressure [Kunkel, 1989] or assuming constant RH with increases in elevation [Wigmosta et al., 1994] are closer to representing the decreased moisture at elevation, yet performance is limited by either the complex topography of Yosemite or days that do not show a linear decline in dew point with elevation. PRISM [Daly et al., 2008] shows monthly-determined lapse rates within the ARB and Yosemite. While these lapse rates do not capture daily variability, the PRISM method of weighted observations does come close to reproducing overall moisture trends within the basin. Both assuming that the dew point is the minimum daily air temperature [Running et al., 1987] and employing an aridity correction to this minimum temperature [Kimball et al., 1997] have a small median bias, but long tails to the error distribution (Figure 5), and as such, error on some days (Figures 3b and 4b) can be quite large. Radiosonde data do not always capture the moisture variations in the basin, indicating that humidity in the mountains cannot be well predicted by the vertical structure of humidity atmospherically upstream. The WRF mesoscale model [Skamarock and Klemp, 2008] performed well in both the ARB and Yosemite.
4.2. Overall Performance of Methods of Generating Dew Point Temperatures
 Figure 5 displays the performance of methods of generating dew point temperatures (a) within the ARB for water years 2008–2010 and (b) within the Yosemite area for water years 2003–2005, using histograms of the error between daily-averaged modeled data and daily-averaged observations. The histograms show all available data, although median biases and boxplots (Figure 6) were calculated for only October-June to match the WRF period of record.
 When one measurement of dew point temperature is available within a basin, empirical methods of extrapolation across a basin are dependent on both the choice of the base station, and whether the modeled lapse rate fits the observed lapse rate. Due to the typically limited availability of stations measuring dew point temperatures in mountain regions, we used the Sacramento and Fresno airport stations to represent available data in the ARB and Yosemite areas, respectively. These stations are near sea level, at an elevation below all stations within the basins. They are also closer to the maritime influence of the ocean than higher elevations to the east. Assuming a constant mixing ratio with elevation [Cramer, 1961] results in a wet bias, with a median bias value of 4.7°C in the ARB and 9.9°C in the Yosemite area. The similar assumption of a −l.25°C km−1 dew point temperature lapse rate from the base station [Franklin, 1983] results in median wet bias values of 4.4°C in the ARB and 9.5°C in the Yosemite area. Seasonally varying adjustments to the actual vapor pressure losses with elevation [Kunkel, 1989] improve upon these methods with a greater rate of moisture loss in the basin, displaying a median dry bias of −1.8°C in the ARB and −0.3°C in the Yosemite area. Assumptions of constant RH [Wigmosta et al., 1994] also represent moisture loss in the basin, with a dry bias of −0.6°C in the ARB and −0.8°C in the Yosemite area.
 Because PRISM data [Daly et al., 2008] are available in monthly-averaged maps, we compared these data to monthly-averaged dew point temperatures, so as to not introduce errors due to daily fluctuations that the model does not claim to represent. On this coarse resolution, the PRISM data performed better than other empirical techniques in the ARB, with a median bias of −0.3°C in the ARB and 3.3°C in the Yosemite area (Figure 6).
 Empirical algorithms for cases when no dew point temperature measurements are available depend on the reliability of air temperature. Assuming that the dew point temperature is equal to the nighttime minimum temperature [Running et al., 1987] results in a median wet bias in both basins, of 1.8°C in the ARB and 0.9°C in the Yosemite area. Using an aridity correction on this minimum daily temperature [Kimball et al., 1997] results in a median wet bias of 1.1°C in the ARB and a dry bias of −0.7°C in the Yosemite area. We note that the graphs (Figure 5) are skewed toward positive bias. In the case of the Running et al.  model, this is expected as the dew point is set to the minimum air temperature; yet in arid environments the minimum air temperature is often higher than the dew point. Kimball et al.  accounts for this with aridity corrections; however, in our study sites, this did not completely resolve the positive bias. Note that these statistics are calculated assuming temperature is directly measured at each verification location. In most situations temperature would also need to be extrapolated across the basin, likely increasing errors.
 Radiosonde data were used to assess whether upwind upper-air measurements represent atmospheric moisture patterns within a basin. These data were dry-biased, with a median bias of −6.5°C in the ARB and −8.5°C in the Yosemite area.
 The WRF model [Skamarock and Klemp, 2008] resolves atmospheric physics and dynamics and matches observed dew point temperatures in both basins well, with a median bias of −0.9°C in the ARB and −1.0°C in Yosemite, for the time period of October-June.
 The interquartile ranges highlight likely errors in performance beyond the median bias. The range in performance is due to variance between days (or months) and between all of the stations in the data set. Figure 6 shows a boxplot of the errors between monthly-averaged estimated data and monthly-averaged observations, and between daily-averaged estimated data and daily-averaged observations for all stations (a and b) within the ARB for water years 2008–2010, October-June data (to match the WRF period of record), and (c and d) within the Yosemite area for water years 2003–2005, October-June data.
 Smaller interquartile ranges of monthly-averaged dew point bias indicate consistent model errors. However, the larger interquartile range in daily-averaged dew point bias indicates that there is significant variability in moisture trends both on a daily basis and between stations in this study location. To highlight this error, we consider that while the Kunkel  algorithm only had a median bias of 0.3°C in the Yosemite area, the interquartile range of daily bias values was 5.2°C. Using monthly-averaged data, the PRISM model had an interquartile range of 1.8°C in the ARB and 3.4°C in Yosemite. While the assumption that the dew point temperature is the minimum air temperature [Running et al., 1987] was biased by 1.8°C in the ARB, the interquartile range was 6.3°C. The other empirical algorithms which use air temperature showed similar magnitudes of potential error. Radiosonde data are not often a reliable predictor of dew point temperature, with interquartile bias ranges of 11.3°C in the ARB and 12.4°C in the Yosemite area. Thus, nearby free-air measurements are not an appropriate representation of the basins' moisture the majority of the time. The WRF model is more accurate in representing daily data a greater amount of the time and for a greater number of stations, showing a smaller interquartile range of dew point temperature bias, 3.3°C in the ARB and 4.1°C in the Yosemite area.
 The performance of the algorithms and models varied seasonally. Figure 7 shows the biases in daily-averaged modeled data for the winter (December-February), spring (March-May), and summer (June-August). The efficacy of dew point lapse rate methods of projecting from a base station varies seasonally. For example, in the Yosemite area median biases vary up to 5.6°C between winter and summer. Empirical methods based on air temperature display wetter dew point biases in the summer; the aridity correction [Kimball et al., 1997] reduced this absolute bias. Radiosonde data's absolute biases increased dramatically during the warmer months. The Yosemite area experienced a larger amount of seasonal variation than the more geographically simple ARB.
4.3. Factors That Affect Estimation of Dew Point Temperatures in the Sierra Nevada
 As illustrated in Figures 3 and 4, the observed dew point temperature patterns can vary dramatically from 1 day to the next, so we investigated the mean patterns and which weather patterns led to deviations from this mean. On average, dew point temperatures declined linearly with elevation in the Sierra Nevada. The median dew point temperature lapse rate was −5.3°C km−1, averaged over water years 2008–2010 in the ARB. Median dew point temperature changed −6.9°C km−1, averaged over water years 2003–2005, in the Yosemite area. For reference, the average annual air temperatures displayed lapse rates between −6.3°C km−1in the ARB and −6.4°C km−1 up the west slope of Yosemite. During the summer, moisture changes with elevation were smaller than in the winter. In both regions, dew point temperature lapse rates were on average 2.5°C km−1 smaller in magnitude during the summer than the winter. This means that there were smaller moisture declines with increases in elevation in the summer.
 Plots of elevation versus dew point temperature display a breakdown between the dew point trends at higher- and lower-elevation stations in the Yosemite area (Figure 4). Above 2000 m, moisture decreases more rapidly with elevation than at lower elevations. Below 2000 m stations report as little as 3°C km−1 change in dew point temperature with elevation during the late spring and early summer.
 While dew point temperatures declined with elevation, daily dew point temperatures often did not follow a linear pattern. We determined the fraction of time a linear lapse rate was a good description of the observed pattern by calculating the RMSE of the observations to the best fit line through those observations, for the ARB, the total Yosemite area, and the Yosemite stations above 2000 m. In the ARB, dew point temperatures generally followed linear trends with elevation; this was less common in the Yosemite area (Table 4). When the analysis was restricted to stations above 2000 m in the Yosemite area, a more consistent linear trend was observed with elevation.
Table 4. RMSE of Daily-Averaged Dew Point With Elevationa
Demonstration of linear trend of dew point temperature with elevation, to a greater extent in the ARB than YOS 1°C to 2°C is not shown.
<1°C over 2000 m
 We examined how well the dew point data fit a linear approximation as functions of precipitation (Figure 8a), average relative humidity (Figure 8b), and dominant wind direction. Days with rain had smaller RMSE values (Figure 8a), with median values of 0.7°C in the ARB (253 observations) and 0.9°C in Yosemite (169 observations) as compared to days without rain, with median values of 1.3°C in the ARB (820 observations) and 1.6°C in Yosemite (925 observations). Similarly, days with a better fit to a linear trend (RMSE < 1°C) occurred when RH was closer to saturation (median RH of 84% in the ARB and 80% in Yosemite), while days with a poorer linear trend (RMSE > 2°C) were drier (median RH of 45% in the ARB and 44% in Yosemite; Figure 8b). Mean winds from reanalysis composites indicated that in both the ARB and Yosemite, days with a good linear fit between dew point temperatures and elevation (RMSE < 1°C, 396 days in the ARB, 181 days in Yosemite) occurred in conjunction with strong westerly winds, while days with a weak linear fit between dew point temperatures and elevation (RMSE > 3°C, 113 days in the ARB, 275 days in Yosemite) occurred during either weak winds or easterly winds from the drier continental side of the range.
4.4. Impacts on Hydrology
 We illustrate the impact of dew point temperature errors of ±2°C on snow disappearance date and annual streamflow with the DHSVM calibrated to the Upper Tuolumne River Basin (above Tuolumne Meadows) during the 7 year period during water years 2003–2009. Figure 9 and Table 4 show the modeled average impacts of a ±2°C dew point temperature change to observed dew point temperatures over the study period in terms of annual average incoming longwave radiation (Figure 9a), annual average latent heat flux (Figure 9b), and total annual sublimation (Figure 9c). Figure 9d illustrates the impact of a ±2°C dew point temperature change for the time period from 1 May to 1 August 2005 on timing of snowmelt and modeled streamflow (Figure 9e). With a 2°C increase in dew point temperatures, we observed a 2 W m−2 increase in estimated incoming longwave radiation, a 0.2 mm d−2 decrease in estimated sublimation, snow disappearing 3 days earlier, and a 1% increase in modeled cumulative annual streamflow. With a 2°C decrease in dew point temperatures, we observed similar changes in the opposite directions (Table 5). While these will differ depending on the basin dynamics, this one example is intended to demonstrate the expected magnitude of impacts of dew point estimation errors on modeling a physical system.
Table 5. Average Annual Changes in Longwave Radiation, Latent Heat Fluxes, Daily Sublimation Rates, Streamflow in the Upper Tuolumne Basin and Snow Disappearance Date Shift in the Upper Tuolumne Meadows in YOS With a ±2°C Change in Dew Point Temperaturea
Dew point Change
Sublimation rates are presented for the ablation season.
2.4 W m−2
−2.3 W m−2
Latent heat flux
−0.7 W m−2
0.9 W m−2
−0.2 cm d−1
0.2 mm d−1
Snow disappearance date, Dana Meadows
3 days earlier
3 days later
Net annual Tuolumne River streamflow volume
 The impacts of dew point estimation errors will vary depending on the characteristics of the basin modeled. The Tuolumne river basin is a high-elevation water-limited basin, with a short growing season and little vegetation. Annual ET each year is controlled primarily by water availability instead of the energy balance, keeping annual ET rates low [Lundquist and Loheide, 2011]. In this basin, the primary impacts of dew point estimation errors are energy balance impacts on snow. With lower dew point temperatures, more water is lost to sublimation, but at the same time, the remaining snowpack is cooled by the latent heat required for sublimation, while lower dew point temperatures also decrease incoming longwave radiation. Thus, the net effect is that the snowpack melts more slowly.
 In the Yosemite area, a ±2°C dew point temperature shift is on the small side of errors observed (Figure 5). Larger errors in dew point estimation would further increase the effects on streamflow volume and snow disappearance date. However, greater dew point temperature shifts were not shown in this example, as they increased the dew point above the air temperature frequently, resulting in supersaturation conditions to an unphysical extent. Since dew point estimation errors increased during the summer, basins with hydrology driven in a larger part by evaporation would likely see increased model error.
5. Summary and Discussion
5.1. Summary of Results
 We tested dew point estimation methods in the ARB and in the Yosemite National Park area along the western slopes of the Sierra Nevada. Empirically derived lapse rates are typically used to extrapolate one low-elevation dew point measurement through the basin. The use of airport stations to represent the low-elevation station was illustrative, as these stations provide a long-term, consistent data set and may be predominantly used both to provide a reliable historical data source, and for future climate sensitivity studies. We chose base stations west of the mountains both because we were examining gradients along the west slope of the range and because winds are predominantly westerly in this region. However, the Sierra Nevada separate moist maritime air to the west from dry desert air to the east. Thus, while utilizing a base station west of the mountains resulted in a wet bias in most cases, a base station located in the arid climate east of the mountains would display a dry bias.
 Errors resulted when the lapse rates did not follow the moisture trends within the basin. Both the Franklin  assumption of a −1.25°C km−1 dew point temperature lapse rate and the Cramer  assumption of a well-mixed air layer did not result in sufficient modeled decrease in moisture over the mountain range. Median biases in these methods were up to 9.9°C in the Yosemite area. This indicates that the distribution of moisture with elevation in the Sierra cannot be determined by the assumption of an air parcel rising adiabatically along the mountain slope.
 Improvements were found with the Kunkel  algorithm and the assumption of constant relative humidity, which represent a more rapid rate of moisture loss with elevation. PRISM improves upon these methods, which were derived from data in other regions, by using multiple local observations to determine the local lapse rate. However, PRISM was more successful in the ARB (bias = −0.3°C) than in the Yosemite area (bias = 3.3°C). Dew point temperature decreased less rapidly with elevation during the warmer months, affecting the performance of these empirical methods. The Franklin  and Cramer  assumptions showed improved performance during the spring, while the assumptions of constant relative humidity and Kunkel  performed better during the winter. PRISM captured monthly trends due to using an empirical fit to local data; performance was consistent across all seasons. However, the low count of stations at elevation [Lundquist et al., 2003] likely reduces the density of input stations to PRISM and impacts performance. While PRISM is designed to represent monthly-averaged trends, we note that daily data sets of dew point temperature could be constructed with sufficient daily observations [Di Luzio et al., 2008].
 Empirical algorithms [Kimball et al., 1997; Running et al., 1987] that derived dew point from air temperature showed a seasonal variation in performance. Both methods were dry-biased on average during the winter in both the ARB and Yosemite. In the more arid summer, both methods had wet biases in the ARB (as large as a 8.1°C median bias for the Running et al.  method), but only the Running method was wet biased in Yosemite. These numbers represent a best case scenario for these methods, as we used local temperature at each measurement point to predict the local dew point. If the locally estimated dew point must also be projected to another location in the basin (following one of the lapse-based methods described earlier), the errors are likely to be compounded.
 Assuming uniform advection of the vertical moisture structure above Oakland (close to the Pacific Ocean) does not represent the observed moisture patterns in the Sierra Nevada well. Radiosonde readings showed large biases from observations and a wide range of day-to-day error. Dry biases were particularly large during the summer (median of −9.9°C in the ARB and −13.0°C in Yosemite). During the summer, high pressure and an inversion are common over California, and air is not well mixed between the Pacific and the Sierra Nevada [Iacobellis et al., 2009]. Furthermore, transpiration likely increases near-surface moisture relative to the free air at this time of year. Our direct horizontal extrapolation of radiosonde readings to compare to observations did not include mixing of air layers; in this case the higher-altitude air above Oakland was decoupled from the marine layer and biased dry compared to the air at the mountain surface.
 WRF, which used a reanalysis product based on the Oakland sounding data for boundary conditions, modeled mixing of air masses and greatly improved on the free-air data, performing well in representing both the overall trends in the basin (with median biases of −0.9°C in the ARB and −1.0°C in Yosemite) and displaying the smallest range of error throughout the October-June period. WRF is able to represent cloud dynamics, such as decreases in the dew point temperature as precipitation forms and falls out of a saturated air mass (Figures 3 and 4), as well as atmospheric dynamics, such as changing wind speeds and directions (and hence differential moisture advection) with height. One additional advantage of WRF is that it is internally consistent, maintaining physical relations between air temperatures and dew point temperatures as water condenses and evaporates. If air temperatures and dew point temperatures are independently calculated from empirical lapse rates, the possibility exists for extrapolated dew point temperatures to exceed air temperatures, which would be an implausible representation of supersaturated air due to the neglect of calculating moisture condensation.
 Empirical models that use projections from a point measurement assume that dew point temperatures follow a linear trend with elevation. This assumption was valid only part of the time at our study sites. Linear dew point temperature trends were more likely during days with precipitation or high humidity.
5.2. Comparison Between Basins
 In general, the empirical models had more difficulty representing dew point temperatures in the Yosemite region than they did in the ARB (Figures 5 and 6). Part of this problem was due to the greater frequency of nonlinear dew point distributions with elevation in the Yosemite region (Table 4) and specifically, to the frequently different slopes of dew point temperature with elevation for groups of stations above and below 2000 m in the Yosemite region illustrated in Figure 4.
 While a full analysis of the causes of these differences is beyond the scope of this study, we expect they are related to basic differences in topography between these regions, as illustrated in Figure 10. At a broad scale, air masses encountering the northern Sierra Nevada (i.e., the ARB) rise smoothly from the central valley to the crest (Figure 10a), resulting in fairly linear patterns of most atmospheric variables. In the southern Sierra Nevada (i.e., the Yosemite region), air masses rise and fall before reaching the Sierra crest. In the case of Yosemite, the Clark range separates the Merced River Basin to the southwest and the Tuolumne River Basin to the northeast (Figure 2). This configuration likely makes the Tuolumne Basin drier by several mechanisms. First, air masses following the typical wind direction will sink over the Tuolumne Basin, causing a local drying and rain-shadow effect. Second, this depression in the large-scale topography likely results in separation of the higher-elevation Tuolumne basin from the moister air to the west. This flow separation may be evidenced in the form of frequent inversions and cold-air pools forming in this high-elevation depression (described for Tuolumne specifically by Lundquist and Cayan  and Lundquist et al. ).
 Flow separation may also be evidenced in the form of mountain-range-wide airflow patterns. Specifically, the southern Sierra Nevada extends to higher elevations than the northern Sierra Nevada, resulting in more frequent blocking of southwesterly wind, which is channeled into mountain-parallel barrier jets [Neiman et al., 2010]. Thus, low-elevation sites are likely exposed to air advected from low elevations to the south, whereas higher-elevation sites are more likely exposed to air advected from the west. This flow separation sets up moisture influences at higher elevations that differ from lower elevations, which likely results in a break in the linear lapse rate. While the full dynamics of this pattern are beyond the scope of the present study, WRF is the only methodology examined that consistently represents this change in lapse rate (or curvature) with elevation correctly. In complex terrain, significant improvements in these modeling representations can be made by running WRF, which captures these dynamics [Hughes et al., 2012], or by including enough higher-elevation measurement stations to resolve the observed daily changes in the dew point lapse rate.
5.3. Implications of Results: The Effects of Biased Dew Point Temperatures
 We tested the effects of dew point estimation errors of ±2°C on streamflow simulations in a high-elevation basin (>2600 m) within our Yosemite study area. Because this area is snowmelt driven, the primary impacts of dew point errors were on the snowpack simulation. Higher dew points increased estimates of downwelling longwave radiation (from the higher moisture content and hence, emissivity, of the atmosphere) and decreased modeled sublimation (by decreasing the vapor pressure deficit), which in turn, resulted in less cooling from the accompanying latent heat flux. The net effect was an increase in melt rates and a shift in streamflow timing toward earlier in the year (Figure 9). Lower dew points had the opposite effect on each process, resulting in slower melt and later streamflow timing (Figure 9). While the overall effects of ±2°C biases were not large (±3 days shift in snow disappearance), many of the methods tested resulted in much larger dew point biases for this basin (10°C for the Cramer and Franklin methods and 8°C for the Running method in the summer in Yosemite), which would have larger impacts on snow and melt timing.
 Most of the Sierra Nevada is moisture-limited, and so while streamflow volume and net annual ET are likely not sensitive to dew point temperature errors, many ecological processes will be. For example, the vapor pressure deficit is a critical parameter in determining fire danger, and many ecological communities are sensitive to desiccation when the vapor pressure drops below a critical value [Rorig and Ferguson, 1999; Grantz, 1990]. Errors in estimating dew point temperatures increased in the summer for most methods (Figure 7), and these errors are likely to have broader reaching impacts than those we illustrated here for snow.
 In sum, our results indicate that (1) empirical assumptions calibrated for other study sites may not be appropriate in the Sierra Nevada, (2) the assumption of a linear trend of dew point temperatures with gains in elevation is not always appropriate in the Sierra Nevada, and (3) the WRF model significantly improves on both free-air readings and empirical techniques in representing dew point temperatures within the basin. The topographic differences between the two study sites were illuminated by the poorer performance of algorithms in the Yosemite area. Although our results were influenced by the Sierra Nevada's location separating moist marine air to the west from drier continental air to the east, we expect similar issues along most of the American Cordierra, which extends from South America to Alaska.
 Our study highlights the importance of both observations within a basin and recognizing topographic limits on the use of simple models. When modeling a geographically simple basin such as the ARB, one base station within the basin paired with PRISM lapse rates will be representative of overall moisture trends most of the time. Use of a high-elevation station that records atmospheric moisture reduces average modeled bias in a basin. However, if the basin is more geographically complex, with air masses due to not only predominant weather patterns, but also microtopography effects and transport along the mountain range, a physically resolved model such as WRF improves representations of dew point variations.
Appendix A: Atmospheric Moisture Metrics and Calculations
 We outline metrics used to determine atmospheric moisture content and how we calculated dew point temperature. The actual amount of water in the air can be viewed as the mixing ratio (R, g kg−1 or kg kg−1), which is the ratio of the mass of water to the mass of dry air. The amount of water in the air can also be given as the actual vapor pressure (Ea, Pa) of water in the air. This relates to the mixing ratio and local air pressure (p, Pa) through the equation [Glickman, 2000]:
 At a given temperature, there is potential for the atmosphere to hold a given amount of water. This maximum water vapor that the air can hold, called the saturation vapor pressure (Esat, Pa), is defined by the pressure and temperature dependence of the relation between the liquid and gas phases of water. A large number of methods have been proposed to determine the saturation vapor pressure from air temperature (T, °C) based on empirical or theoretical derivations [Lawrence, 2005]. We employ the Magnus-Tetens formula [Murray, 1967] with empirically updated coefficients [Alduchov and Eskridge, 1996]. The formula, shown here, was found to err less than 0.4% for the temperature range of −40°C–50°C [Lawrence, 2005]:
 In hydrological applications, we are often concerned with the ratio of the amount of water in the atmosphere over the amount of water that the atmosphere can hold. This ratio is called the relative humidity (RH, %) and can be defined as
 The dew point temperature (TD, °C) is the temperature at which the air will be saturated for a given amount of water vapor. This can be calculated from the actual amount of water vapor in the air (Ea) as determined from relative humidity and the Magnus formulation for vapor pressure at the dew point temperature:
 This can be solved to a formulation that takes inputs of commonly measured variables, relative humidity, and air temperature:
 The dew point depression can be used to view the measure of the difference between actual and potential water vapor content in terms of temperature. This is calculated as the dew point temperature subtracted from the air temperature.
 For instrument deployment and retrieval, we thank Mark Raleigh and Courtney Moore for help in the ARB and Dan Cayan, Mike Dettinger, Brian Huggett, and Jim Roche for help in Yosemite. We also thank Nic Wayand and Mimi Hughes for help with WRF data acquisition and processing. Funding was provided by NSF through grant EAR-0838166 and by NOAA through their Hydrometeorological Testbed and through the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) under NOAA cooperative agreement NA17RJ1232 and NA10OAR4320148, where this paper is contribution 1883.