a. Water consumption related to human activity

A number of data sources were reviewed that contain partial information on the amount of water consumed in various types of human activities. In the end, it was determined that the U.S. Geological Survey (USGS) was the most comprehensive source, providing annual water consumption data for all counties in the United States, organized by the type of activity. The compilation is performed by USGS every 5 yr. At the time this study was conducted, the most recent compilation was the one released in 2004 for the year 2000 (Hutson et al. 2004). The analysis described in this paper makes use of the USGS data from 2000.

b. Temporal variation in anthropogenic moisture

The USGS data quantify the amount of water used in each county in the United States, but only as an annual total. Ingesting anthropogenic moisture into WRF requires that the water be distributed on the forecast grid, in amounts appropriate to the forecast period. This necessitates allocating the water used in human activities to specific locations and at specific times. A number of approaches to this problem were assessed. Temporal variation is inferred using statistics on evapotranspiration regions in California. Spatial distribution, described in the next subsection, is inferred based on satellite-derived land-use categories.

The Office of Water Use Efficiency in the California Department of Water Resources (DWR), in cooperation with the University of California, Davis, manages a network of automated weather stations under the California Irrigation Management Information System (CIMIS) program. The CIMIS program was initiated in 1982 and has installed and operated 177 automated weather stations, of which 130 are currently active.

CIMIS automated stations collect data at 60-s intervals, and average them for hourly and daily periods. The data are uploaded daily to CIMIS’s central databases. The data are then ingested in an evapotranspiration model for two reference vegetation types: grass and alfalfa. The model computes daily evapotranspiration amounts, which are used by growers and large landscaping organizations to manage their irrigation. Details of the CIMIS program are available on the DWR Web site (DWR 2007).

Based on long-term studies of CIMIS data, DWR has compiled monthly and annual evapotranspiration amounts for a set of 18 zones that cover California. These zones are shown in Fig. 2. Many growers and large landscaping companies determine their irrigation amounts from the CIMIS data. As a result, there is good reason to expect that both commercial irrigation and domestic use, in the form of watering large landscape projects, track the CIMIS data. It was decided that monthly CIMIS evapotranspiration amounts, normalized by the annual total evapotranspiration, provided an acceptable way to allocate annual anthropogenic moisture to each month. As expected, the evapotranspiration fraction is strongly influenced by seasonal variation and, to a lesser extent, by the type of climate. Two examples are shown. The first example, in Fig. 3, shows the monthly evapotranspiration fraction for the zones that are found in Orange County, a typical coastal county. Figure 4 shows the monthly evapotranspiration fraction for the zones that are found in Imperial County, a hot inland desert county. The more moderate coastal climate is evident in Orange County, particularly in the summer.

c. Spatial distribution of anthropogenic moisture

The last step in creating an anthropogenic moisture database is to distribute the moisture spatially. This has been done using satellite-derived land-use information. While a number of such databases exist, it was decided to use the same land cover characterization (LCC) maps as are used in WRF, at the 30″ resolution. The WRF LCC database is a version of the USGS Global Land Cover Characteristics dataset (USGS 2005). It provides land use globally at a spatial resolution of 30″ (926 m) in 24 categories. Of these, there is one category for urban land use, and four categories of irrigated croplands, namely irrigated cropland and pasture, mixed dryland–irrigated cropland and pasture, cropland–grassland mosaic, and cropland–woodland mosaic. Irrigated and urban LCC pixels were mapped to California counties and to DWR evapotranspiration zones. The numbers of irrigated and urban pixels in each county that are in each evapotranspiration zone were calculated.

From this, an area-weighted, average monthly fraction of annual evapotranspiration was determined for each county, separately for both urban and irrigated land-use types. USGS annual amounts for commercial irrigation and domestic use were then multiplied by their respective monthly evapotranspiration fractions to determine the monthly amounts of anthropogenic moisture for each county. These amounts were assigned to each urban or irrigated pixel, in each county, as appropriate. It was assumed that there would be equal amounts of the monthly anthropogenic moisture for each day in the month.

Plots of anthropogenic moisture, showing monthly average values of equivalent daily precipitation, in tenths of millimeters per day, are shown in Figs. 5 through 8, for the months of December, March, June, and September, respectively. As can be seen, there is a significant area that receives nonnegligible equivalent precipitation, especially in the summer, when natural precipitation averages less than 1.5 mm month⁻¹ over most of the domain. In fact, overall in California, 24 of the 58 counties have a combination of urban and irrigated area in excess of 10% of the total area of the county. Ten counties have a combination of urban and irrigated area of 25% or more of the total area of the county. Within the inner domain there are four counties, Kern, Imperial, Los Angeles, and Orange that have a combination of urban and irrigated area in excess of 10% of the total area of the county. Nearly all of the urban and irrigated area in California receives at least 1 mm day⁻¹ of equivalent precipitation, even in December.

a. Domain and model description

Version 2.2 of the ARW model was used in this study. It is configured to use the Eta–TKE follow-on planetary boundary layer scheme, and the Noah land surface model, with temperature and moisture predicted in four soil layers. The 15-km-grid outer domain and 5-km-grid inner domain were initialized using terrain data derived from the 30″ USGS LCC dataset. One-way interaction was allowed from the outer to the inner domain. The model atmosphere uses 37 vertical levels, with a top pressure of 100 hPa. Short- and longwave radiation are parameterized using the Dudhia and the Rapid Radiative Transfer Model (RRTM) radiative transfer schemes, respectively (Dudhia 1989; Mlawer et al. 1997). Cloud and precipitation effects are modeled using the cumulus parameterization of Kain–Fritsch (Kain and Fritsch 1990, 1993; Kain 2004), and the WRF single-moment, five-class, microphysics scheme (Hong et al. 2004). The initial and lateral boundary conditions are provided by the National Centers for Environmental Prediction (NCEP) North American Model (NAM), at 40-km grid spacing.

b. Model modifications

By modifying the WRF Registry space was made available in WRF to hold the field of the spatially distributed anthropogenic liquid at the surface, for the middle of each month of the year, as well as the instantaneous field at each simulation time. The instantaneous field is derived from the monthly field by linear temporal interpolation. The WRF Preprocessing System (WPS) is used to ingest the anthropogenic liquid data and to interpolate them to the domain grids. WPS then puts the results into the WRF input file, from which WRF makes them available to the surface physics routines, where they appear as extra liquid flux only at the surface. As such, it enhances the surface evaporation and evapotranspiration, as well as accumulating on the surface, percolating into the soil, and adding to surface runoff. In this first attempt to represent the effects of anthropogenic moisture, it was specified as a steady source throughout each day.

Unlike MM5, WRF contains an urban canopy submodel that can be included or not. The results presented here were generated including the urban canopy submodel.

a. Determining the statistical significance of differences in bias and MAE

Let O_ijk be the observation of a parameter at simulation day i, at location j, and at hour k. Similarly, let and be the forecast values of the same parameter in simulations for the control and modified cases. Let errors in the forecast control and modified values be denoted by and , respectively, and the absolute values of the errors by and .

Since the same procedure is followed to evaluate the statistical significance of the differences between the control and modified cases, for both the bias and the MAE, it is convenient to describe it generally. Let represent either or , and similarly for the control case with . Let n_ik be the number of observations at simulation day i and hour k. Let 〈·〉 represent the average over all locations of a parameter that depends on simulations hour, location, and day in the set of observations being considered, of which there are several. Thus, for example, for a parameter θ,

View Expanded

Let . The mean of Δ_ik over the sample of 30 simulation days is

View Expanded

where the overbar represents an average over simulation days. Though the distribution of the Δ_ik is unknown, for the surface parameters considered in this study, a sample of 30 was taken to be large enough for the central limit theorem to apply, implying the distribution is normal. For a given simulation hour k, the time series of Δ_ik is serially correlated. Consequently, in the test to determine whether Δ_k is significantly different from zero, and thus whether x_k^m is different from x_k^c, the variance of Δ_ik over the sample of simulation days must be modified by the factor

View Expanded

where ρ₁ is the lag-one autocorrelation of the series Δ_ik over the simulation days. The null hypothesis is that the population mean of Δ_ik (for fixed k) is zero. The sample statistic used to test the null hypothesis is thus

View Expanded

where V_k is the variance of Δ_ik over the simulation days (Wilks 2006).

If |z| > 1.654, then the null hypothesis is rejected, and the difference in means is significant at the 5% level. On average, at most 1 in 20 identical experiments will yield a z of comparable magnitude.

b. Surface temperature bias and MAE verification over the entire domain

When taken over the entire domain for the 30 days of the study, the hourly verification results show a statistically significant reduction in the forecast temperature bias from the morning through early afternoon. Note that, while the impacts on the model temperature were shown to be much larger on the skin temperature rather than those on the shelter height temperature, the latter are used for verification because that is the parameter available in the surface observation data. Figure 12 shows the bias in temperature compared to AFWA stations, over the entire model domain. The biases of the control case (i.e., without anthropogenic moisture) and the modified case both exhibit strong diurnal variation, and are comparable for most hours except for the morning through early afternoon hours [0400 local time (LT) through 1500 LT]. The difference between the biases is greatest at hour 19 (1200 LT). At that hour, the bias of the control case exceeds that of the modified case by 0.13°C. For hours 26 (1900 LT) and 27 (2000 LT), the magnitude of the bias of the control case is 0.1°C less than that of the modified case. The largest magnitude of the bias, which is negative, occurs at 2000 LT.

It appears that the model cools too rapidly during the evening hours and warms too rapidly during the morning (0600 LT) through early afternoon hours (1400 LT). The addition of anthropogenic moisture slows the rate of heating during this time, and slightly accelerates the rate of cooling from late afternoon through 2000 LT. It should be noted that the largest warm bias is only 0.4°C, which is considerably smaller than the 1°–2°C bias observed with previous integrations of the MM5 model over the same domain and similar time periods.

Next, the verification was limited to the areas with anthropogenic moisture in an attempt to isolate the effects of adding the moisture. Calculation of the bias in temperature was restricted to areas with anthropogenic moisture; the results are presented in Fig. 13. Note that the number of observations used in this verification is about half of the number of observations used for verification over the entire domain. The bias of both the control and modified cases again shows strong diurnal variation, and the two are generally comparable except for the period from simulation hour 15 (0800 LT) to hour simulation hour 22 (1500 LT). During those hours they are as much as 0.2°C apart, which is only slightly larger than for the unrestricted domain comparison. The overly rapid warming seen in the control and modified runs in the morning is not evident over those land types affected by anthropogenic moisture. This may be due to the radiative properties specified for these land-use types.

For shelter temperature MAE verification for the entire domain (Fig. 14), only those hours from late morning to early evening have an MAE for the anthropogenic moisture case that is less than that of the control case. Though the improvement in MAE is small during this period, the differences at 1200, 1500, 1700, and 1800 UTC (0500, 0800, 1000, and 1100 LT) are statistically significant.

The shelter temperature MAEs, computed for both cases, using AFWA data restricted to those areas where anthropogenic moisture was added, are shown in Fig. 15. As with the verifications over the entire domain, the only time when the MAE for the anthropogenic moisture case is less than the control case is from late morning to early afternoon. Though these differences are small, they are statistically significant. There also is a statistically significant reduction of the MAE in the modified case in the early morning hours (0200–0300 and 1900–2000 LT) of the second day of the forecast period. This reduction may be caused by reduced cooling due to the reduction in outgoing longwave radiation that is due to the continued moistening of the lower atmosphere over the inland valleys in the modified case. During the early morning hours of the first day of the forecast, it appears that sufficient moistening of the atmosphere has not occurred to reduce radiative cooling to the levels where this effect predominates over evaporative cooling. This results in higher MAEs for the modified case than the control case during the early morning hours of the first forecast day, but this difference is not statistically significant.

c. Water vapor mixing ratio verification over the entire domain

Verification was performed on the forecast water vapor mixing ratio, using reports from the 31 available AFWA surface stations as truth. AQMD stations do not report variables from which the water vapor mixing ratio may be determined, so no verification was possible with the AQMD station set. Here again, the biases are comparable for the two cases over the entire domain. Taken over all available days and hours, the bias for the control case was −0.326 g kg⁻¹, while the bias for the modified case was −0.416 g kg⁻¹. Note that most of the AFWA observations of mixing ratio are made only every 6 h, at the times of major and minor synoptic observations.

d. Surface temperature verification for a station within an irrigated area

The largest anthropogenic moisture amounts occur in commercially irrigated regions. The station at the Bakersfield airfield is located in a region in the Central Valley that is extensively irrigated. Averaged over all days and forecast hours, the control case had a bias of −1.57°C versus −2.36°C for the modified case, so the overall effect of the anthropogenic moisture in the modified case was to cool the model atmosphere significantly at this station. Figure 16 shows the bias for the control and anthropogenic moisture cases, as a function of forecast hour, computed for the sample of 30 paired simulations. The addition of anthropogenic moisture all but eliminated the midmorning to early evening temperature warm bias seen in the control run. However, it exacerbated the early morning cold bias. To see if the difference in biases between the cases was statistically significant at the 95% level, the t test was applied, allowing for the possibility that the variances of the biases differed. In this case the appropriate t test is the two-tailed test, where the null hypothesis is rejected if the magnitude of the sample t statistic exceeds a certain value. It was found that the reduction of the late morning to early evening warm bias at Bakersfield is statistically significant, as are the few degradations that occurred in the evening and early morning hours.

Figure 17 shows the shelter temperature MAE for Bakersfield, as a function of time of day and simulation hour. There is a significant reduction in MAE in the modified case, from late morning through early evening, as compared to the control case. The improvement in MAE for the modified case is nearly 40% for a number of these hours. However a significant degradation in skill in the modified case is evident during evening and early morning hours.

The generally negative temperature bias found at Bakersfield in the control case was surprising, and is what led to a reexamination of the case studies that had initially pointed the way to the perception of a positive bias. The original case studies had mixed results: some had a negative bias while others had a positive bias. Adding anthropogenic moisture generally made the atmosphere cooler, so in the present study it reduced the late morning warm bias. It also made any negative bias more negative.

e. Water vapor mixing ratio verification for a station within an irrigated area

Assuming that a portion of the warm bias seen was due to a lack of anthropogenic moisture in the control case, one would expect to see a corresponding dry bias. Figure 18 shows these conditions are seen in the control case, between the hours of 1500 and 1800 LT, when the warm bias is at its peak. However, much of the daytime warm bias in the control case, from the hours of 0900 to 1300 LT, occurs during periods where there is a moist bias. The addition of anthropogenic moisture does lessen the dry bias during the time of the peak warm bias in the model. However, it also significantly (the same statistical significance testing was used for the mixing ratio as was used for temperature) exacerbates the model moist bias that occurs, from the early morning hours through the early afternoon. It terms of the total humidity forecast error as represented by MAE (see Fig. 19), a slight reduction in MAE is seen in the modified case that corresponds to the reduction of the temperature MAE for this case during the 1500–1800 LT period. However, unlike the reduction in the temperature MAE, where the improvement is statistically significant, the same cannot be said for the mixing ratio.